Problems of number theory in mathematical competitions pdf
Like
Like Love Haha Wow Sad Angry

Math Stuff contrib.andrew.cmu.edu

problems of number theory in mathematical competitions pdf

Combinatorial problems in mathematical competitions. Number Theory Problems Amir Hossein Parvardi ∗ June 16, 2011 I’ve written the source of the problems beside their numbers. If you need solutions, visit AoPS Resources Page, select the competition, select the year and go to the link of the problem., Number Theory is one of the oldest and most beautiful branches of Mathematics. It abounds in problems that yet simple to state, are very hard to solve. Some number-theoretic problems that are yet unsolved are: 1. (Goldbach’s Conjecture) Is every even integer greater than 2 the sum of distinct primes? 2..

Power Putnam Preparation math.toronto.edu

1001 Problems in Classical Number Theory Mathematical. “This is a collection of elementary number theory problems taken mainly from mathematical olympiads and other contests held in different countries, mainly in recent years. … This makes the book a useful source of material for tests, homeworks, projects, and classroom discussion. …, Mathematics is the queen of sciences and arithmetic the queen of mathematics.” At first blush one might think that of all areas of mathematics certainly arithmetic should be the simplest, but it is a surprisingly deep subject. We assume that students have some familiarity with basic set theory….

Number Theory. Camsie's New Job. Here are some of our favorite countdown round problems from the 2019 competitions. School #16 On a certain farm, each chicken has two feet and each rabbit has four feet. If the combined number of chickens and rabbits on the farm is 100 and there are a total of 260 feet on these animals, how many chickens are AbeBooks.com: Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad) (9789814271141) by Yu Hong Bing; Hongbing Yu and a great selection of similar New, Used and Collectible Books available now at great prices.

Number Theory Problems Amir Hossein Parvardi ∗ June 16, 2011 I’ve written the source of the problems beside their numbers. If you need solutions, visit AoPS Resources Page, select the competition, select the year and go to the link of the problem. Number Theory. Camsie's New Job. Here are some of our favorite countdown round problems from the 2019 competitions. School #16 On a certain farm, each chicken has two feet and each rabbit has four feet. If the combined number of chickens and rabbits on the farm is 100 and there are a total of 260 feet on these animals, how many chickens are

Jul 11, 2007 · The heart of Mathematics is its problems. Paul Halmos Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting problems in elementary Number Theory. Many of the problems are mathematical competition problems from all over the world like IMO, APMO, APMC, Putnam and many others. Number Theory is one of the oldest and most beautiful branches of Mathematics. It abounds in problems that yet simple to state, are very hard to solve. Some number-theoretic problems that are yet unsolved are: 1. (Goldbach’s Conjecture) Is every even integer greater than 2 the sum of distinct primes? 2.

The heart of Mathematics is its problems. Paul Halmos 1. Introduction Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting questions in Number Theory. Many of the problems are mathematical competition problems all over the world including IMO, APMO, APMC, Putnam, etc. 101 PROBLEMS IN ALGEBRA FROM THE TRAINING OF THE USA IMO TEAM T ANDREESCU ВЈt Z FEND that these mathematics competition problems are a positive sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinato-

Number Theory Problems Amir Hossein Parvardi ∗ June 16, 2011 I’ve written the source of the problems beside their numbers. If you need solutions, visit AoPS Resources Page, select the competition, select the year and go to the link of the problem. The problems range in difficulty from problems that any alumnus of a class in elementary number theory should be able to do in their sleep, through problems from various math competitions and the kinds of problems one would find in Mathematics Magazine, to problems that professional number theorists will struggle to figure out. One interesting

Number theory is an important research field of mathematics. In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. They are flexible and diverse. In this book, the author introduces some basic concepts and methods in elementary number theory via 2. Read the problems through again and make notes on the six problems: (a) What category of math: calculus, linear algebra, number theory, etc. (b) Underline the data in each problem (c) Estimate the di culty and devise an order of attack. While A-1 and B-1 are usually the easiest in each session, that may not be the case for a given year and

1001 Problems in Classical Number Theory Mathematical

problems of number theory in mathematical competitions pdf

Number Theory MATHCOUNTS. “This is a collection of elementary number theory problems taken mainly from mathematical olympiads and other contests held in different countries, mainly in recent years. … This makes the book a useful source of material for tests, homeworks, projects, and classroom discussion. …, In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. This book introduces some basic concepts and methods in elementary number theory via problems in mathematical competitions..

Problems in Elementary Number Theory math.fau.edu

problems of number theory in mathematical competitions pdf

1001 Problems in Classical Number Theory Mathematical. The problems range in difficulty from problems that any alumnus of a class in elementary number theory should be able to do in their sleep, through problems from various math competitions and the kinds of problems one would find in Mathematics Magazine, to problems that professional number theorists will struggle to figure out. One interesting https://en.m.wikipedia.org/wiki/Millennium_Prize_Problems Jul 23, 2018 · Number Theory Problems in Mathematical Competitions (2015 – 2016) Rating As promised, Amir Hossein is releasing the collection of number theory problems in mathematical competitions held in 2015 – 2016 school year for free..

problems of number theory in mathematical competitions pdf


This books contains about 230 selected problems from more than 45 competitions. These problems are divided into five sections following the classification of the IMO: Algebra, Analysis, Number Theory, Combina-torics, and Geometry. It should be noted that the problems presented in this book are of average level of difficulty. The heart of Mathematics is its problems. Paul Halmos 1. Introduction Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting questions in Number Theory. Many of the problems are mathematical competition problems all over the world including IMO, APMO, APMC, and Putnam, etc.

The heart of Mathematics is its problems. Paul Halmos 1. Introduction Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting questions in Number Theory. Many of the problems are mathematical competition problems all over the world including IMO, APMO, APMC, and Putnam, etc. The book is organized in six chapters: algebra, number theory, geometry, trigonometry, analysis and comprehensive problems. In addition, other fields of math ematics found their place in this book, for example, combinatorial problems can be found in the last chapter, and problems involving complex numbers are included in the tr igonometry section.

Chinese) on Forurzrd to IMO: a collection of mathematical Olympiad problems major mathematical competitions in China, which provides a glimpse on how the China national team is selected and formed. First, it is the China The mathematical topics in the IMO include number theory, polynomials, functional equations, inequalities, graph Number Theory Problems Amir Hossein Parvardi ∗ June 16, 2011 I’ve written the source of the problems beside their numbers. If you need solutions, visit AoPS Resources Page, select the competition, select the year and go to the link of the problem.

AbeBooks.com: Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad) (9789814271141) by Yu Hong Bing; Hongbing Yu and a great selection of similar New, Used and Collectible Books available now at great prices. PROBLEMS IN ELEMENTARY NUMBER THEORY 5 2.2. Sources. 1. 1969 EВЁotvВЁos-KurschВґВЁ ak Mathematics Competition 2. IMO 1988/6 3. 4. Turkey 1994 5. Mediterranean Mathematics Competition 2002 6. IMO 1998/4 7. Unused Problem for the Balkan Mathematical Olympiad

“This is a collection of elementary number theory problems taken mainly from mathematical olympiads and other contests held in different countries, mainly in recent years. … This makes the book a useful source of material for tests, homeworks, projects, and classroom discussion. … Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad Series)€ Publisher: World Scientific Publishing Company (September 16, 2009) Language: English Pages: 116 Size: 29.96 MB Format: PDF / ePub / Kindle Number theory is an important research field of mathematics. In mathematical competitions, problems of elementary

MATHEMATICS COMPETITIONS JournAl of The World federATion of nATionAl MATheMATics coMpeTiTions (ISSN 1031 – 7503) Published biannually by AMT publishing AusTrAliAn MATheMATics TrusT universiTy of cAnberrA locked bAg 1 cAnberrA gpo AcT 2601 AusTrAliA With significant support from the UK Mathematics Trust. Articles (in English) are welcome. Amazon.in - Buy Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad Series) book online at best prices in India on Amazon.in. Read Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad Series) book reviews & author details and more at Amazon.in. Free delivery on qualified orders.

In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. This book introduces some basic concepts and methods in elementary number theory via problems in mathematical competitions. tions of the given problem and further indicate unsolved problems associated with the given problem and solution. This ancillary textbook is intended for everyone interested in number theory. It will be of especial value to instructors and students both as a textbook and a source of reference in mathematics …

Problems in Elementary Number Theory math.fau.edu

problems of number theory in mathematical competitions pdf

Math Stuff contrib.andrew.cmu.edu. In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. They are flexible and diverse. In this book, the author introduces some basic concepts and methods in elementary number theory via problems in mathematical competition, The heart of Mathematics is its problems. Paul Halmos 1. Introduction Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting questions in Number Theory. Many of the problems are mathematical competition problems all over the world including IMO, APMO, APMC, Putnam, etc..

www.albertstam.com

www.albertstam.com. In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. They are flexible and diverse. In this book, the author introduces some basic concepts and methods in elementary number theory via problems in mathematical competition, Jul 11, 2007В В· The heart of Mathematics is its problems. Paul Halmos Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting problems in elementary Number Theory. Many of the problems are mathematical competition problems from all over the world like IMO, APMO, APMC, Putnam and many others..

In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. This book introduces some basic concepts and methods in elementary number theory via problems in mathematical competitions. Number Theory. Introduction to Number Theory: As the name suggests, a handout which goes over some very basic ideas in number theory. While some of the material itself is a bit lacking, the problems I think serve as a good introduction into number theoretic intuition.

2. Read the problems through again and make notes on the six problems: (a) What category of math: calculus, linear algebra, number theory, etc. (b) Underline the data in each problem (c) Estimate the di culty and devise an order of attack. While A-1 and B-1 are usually the easiest in each session, that may not be the case for a given year and The heart of Mathematics is its problems. Paul Halmos 1. Introduction Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting questions in Number Theory. Many of the problems are mathematical competition problems all over the world including IMO, APMO, APMC, and Putnam, etc.

“This is a collection of elementary number theory problems taken mainly from mathematical olympiads and other contests held in different countries, mainly in recent years. … This makes the book a useful source of material for tests, homeworks, projects, and classroom discussion. … Number Theory is one of the oldest and most beautiful branches of Mathematics. It abounds in problems that yet simple to state, are very hard to solve. Some number-theoretic problems that are yet unsolved are: 1. (Goldbach’s Conjecture) Is every even integer greater than 2 the sum of distinct primes? 2.

Mathematics is the queen of sciences and arithmetic the queen of mathematics.” At first blush one might think that of all areas of mathematics certainly arithmetic should be the simplest, but it is a surprisingly deep subject. We assume that students have some familiarity with basic set theory… The heart of Mathematics is its problems. Paul Halmos 1. Introduction Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting questions in Number Theory. Many of the problems are mathematical competition problems all over the world including IMO, APMO, APMC, Putnam, etc.

Problem Books in Mathematics. Book Series Arthur Engels "Problem-Solving Strategies" is good for elementary students and Richard Guys "Unsolved Problems in Number Theory" is the classical advanced prototype. The series also features a number of successful titles that prepare students for problem-solving competitions. Over 10 million Problem Books in Mathematics. Book Series Arthur Engels "Problem-Solving Strategies" is good for elementary students and Richard Guys "Unsolved Problems in Number Theory" is the classical advanced prototype. The series also features a number of successful titles that prepare students for problem-solving competitions. Over 10 million

Vol. 1 A First Step to Mathematical Olympiad Problems by Derek Holton (University of Otago, New Zealand) Vol. 2 Problems of Number Theory in Mathematical Competitions by Yu Hong-Bing (Suzhou University, China) translated by Lin Lei (East China Normal University, China) ZhangJi - Lec Notes on Math's Olymp Courses.pmd2 11/2/2009, 3:35 PM Sep 22, 2013В В· Competition problems Problem (2003 AIME II, Problem 2.) Find the greatest integer multiple of 8, no two of whose digits are the same. Problem (2009 PUMaC Number Theory, Problem A1.) If 17! = 355687ab8096000, where a and b are two missing digits, nd a and b. Problem (2004 AIME II, Problem 10.) Number Theory - Modular arithmetic and GCD

Vol. 1 A First Step to Mathematical Olympiad Problems by Derek Holton (University of Otago, New Zealand) Vol. 2 Problems of Number Theory in Mathematical Competitions by Yu Hong-Bing (Suzhou University, China) translated by Lin Lei (East China Normal University, China) ZhangJi - Lec Notes on Math's Olymp Courses.pmd2 11/2/2009, 3:35 PM The problems range in difficulty from problems that any alumnus of a class in elementary number theory should be able to do in their sleep, through problems from various math competitions and the kinds of problems one would find in Mathematics Magazine, to problems that professional number theorists will struggle to figure out. One interesting

Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad Series)€ Publisher: World Scientific Publishing Company (September 16, 2009) Language: English Pages: 116 Size: 29.96 MB Format: PDF / ePub / Kindle Number theory is an important research field of mathematics. In mathematical competitions, problems of elementary 2. Read the problems through again and make notes on the six problems: (a) What category of math: calculus, linear algebra, number theory, etc. (b) Underline the data in each problem (c) Estimate the di culty and devise an order of attack. While A-1 and B-1 are usually the easiest in each session, that may not be the case for a given year and

Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad) by Yu Hong Bing Paperback $30.60 Only 11 left in stock (more on the way). Ships from and sold by Amazon.com. Vol. 1 A First Step to Mathematical Olympiad Problems by Derek Holton (University of Otago, New Zealand) Vol. 2 Problems of Number Theory in Mathematical Competitions by Yu Hong-Bing (Suzhou University, China) translated by Lin Lei (East China Normal University, China) ZhangJi - Lec Notes on Math's Olymp Courses.pmd2 11/2/2009, 3:35 PM

101 PROBLEMS IN ALGEBRA FROM THE TRAINING OF THE USA IMO TEAM T ANDREESCU £t Z FEND that these mathematics competition problems are a positive sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinato- Number Theory is one of the oldest and most beautiful branches of Mathematics. It abounds in problems that yet simple to state, are very hard to solve. Some number-theoretic problems that are yet unsolved are: 1. (Goldbach’s Conjecture) Is every even integer greater than 2 the sum of distinct primes? 2.

101 PROBLEMS IN ALGEBRA FROM THE TRAINING OF THE USA IMO TEAM T ANDREESCU ВЈt Z FEND that these mathematics competition problems are a positive sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinato- In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. They are flexible and diverse. In this book, the author introduces some basic concepts and methods in elementary number theory via problems in mathematical competition

1001 Problems in Classical Number Theory Mathematical

problems of number theory in mathematical competitions pdf

Combinatorial problems in mathematical competitions. Number Theory is one of the oldest and most beautiful branches of Mathematics. It abounds in problems that yet simple to state, are very hard to solve. Some number-theoretic problems that are yet unsolved are: 1. (Goldbach’s Conjecture) Is every even integer greater than 2 the sum of distinct primes? 2., Sep 22, 2013 · Competition problems Problem (2003 AIME II, Problem 2.) Find the greatest integer multiple of 8, no two of whose digits are the same. Problem (2009 PUMaC Number Theory, Problem A1.) If 17! = 355687ab8096000, where a and b are two missing digits, nd a and b. Problem (2004 AIME II, Problem 10.) Number Theory - Modular arithmetic and GCD.

Number Theory MATHCOUNTS

problems of number theory in mathematical competitions pdf

Problems in Elementary Number Theory math.fau.edu. The book is organized in six chapters: algebra, number theory, geometry, trigonometry, analysis and comprehensive problems. In addition, other fields of math ematics found their place in this book, for example, combinatorial problems can be found in the last chapter, and problems involving complex numbers are included in the tr igonometry section. https://en.m.wikipedia.org/wiki/Millennium_Prize_Problems Jul 11, 2007В В· The heart of Mathematics is its problems. Paul Halmos Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting problems in elementary Number Theory. Many of the problems are mathematical competition problems from all over the world like IMO, APMO, APMC, Putnam and many others..

problems of number theory in mathematical competitions pdf


Sep 22, 2013В В· Competition problems Problem (2003 AIME II, Problem 2.) Find the greatest integer multiple of 8, no two of whose digits are the same. Problem (2009 PUMaC Number Theory, Problem A1.) If 17! = 355687ab8096000, where a and b are two missing digits, nd a and b. Problem (2004 AIME II, Problem 10.) Number Theory - Modular arithmetic and GCD AbeBooks.com: Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad) (9789814271141) by Yu Hong Bing; Hongbing Yu and a great selection of similar New, Used and Collectible Books available now at great prices.

Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad) by Yu Hong Bing Paperback $30.60 Only 11 left in stock (more on the way). Ships from and sold by Amazon.com. Jul 11, 2007В В· The heart of Mathematics is its problems. Paul Halmos Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting problems in elementary Number Theory. Many of the problems are mathematical competition problems from all over the world like IMO, APMO, APMC, Putnam and many others.

The book is organized in six chapters: algebra, number theory, geometry, trigonometry, analysis and comprehensive problems. In addition, other fields of math ematics found their place in this book, for example, combinatorial problems can be found in the last chapter, and problems involving complex numbers are included in the tr igonometry section. Number Theory. Introduction to Number Theory: As the name suggests, a handout which goes over some very basic ideas in number theory. While some of the material itself is a bit lacking, the problems I think serve as a good introduction into number theoretic intuition.

AbeBooks.com: Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad) (9789814271141) by Yu Hong Bing; Hongbing Yu and a great selection of similar New, Used and Collectible Books available now at great prices. This books contains about 230 selected problems from more than 45 competitions. These problems are divided into five sections following the classification of the IMO: Algebra, Analysis, Number Theory, Combina-torics, and Geometry. It should be noted that the problems presented in this book are of average level of difficulty.

PROBLEMS IN ELEMENTARY NUMBER THEORY 5 2.2. Sources. 1. 1969 EВЁotvВЁos-KurschВґВЁ ak Mathematics Competition 2. IMO 1988/6 3. 4. Turkey 1994 5. Mediterranean Mathematics Competition 2002 6. IMO 1998/4 7. Unused Problem for the Balkan Mathematical Olympiad 2. Read the problems through again and make notes on the six problems: (a) What category of math: calculus, linear algebra, number theory, etc. (b) Underline the data in each problem (c) Estimate the di culty and devise an order of attack. While A-1 and B-1 are usually the easiest in each session, that may not be the case for a given year and

This books contains about 230 selected problems from more than 45 competitions. These problems are divided into five sections following the classification of the IMO: Algebra, Analysis, Number Theory, Combina-torics, and Geometry. It should be noted that the problems presented in this book are of average level of difficulty. tions of the given problem and further indicate unsolved problems associated with the given problem and solution. This ancillary textbook is intended for everyone interested in number theory. It will be of especial value to instructors and students both as a textbook and a source of reference in mathematics …

Number Theory Problems Amir Hossein Parvardi ∗ June 16, 2011 I’ve written the source of the problems beside their numbers. If you need solutions, visit AoPS Resources Page, select the competition, select the year and go to the link of the problem. Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad) by Yu Hong Bing Paperback $30.60 Only 11 left in stock (more on the way). Ships from and sold by Amazon.com.

Jul 11, 2007 · The heart of Mathematics is its problems. Paul Halmos Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting problems in elementary Number Theory. Many of the problems are mathematical competition problems from all over the world like IMO, APMO, APMC, Putnam and many others. MATHEMATICS COMPETITIONS JournAl of The World federATion of nATionAl MATheMATics coMpeTiTions (ISSN 1031 – 7503) Published biannually by AMT publishing AusTrAliAn MATheMATics TrusT universiTy of cAnberrA locked bAg 1 cAnberrA gpo AcT 2601 AusTrAliA With significant support from the UK Mathematics Trust. Articles (in English) are welcome.

“This is a collection of elementary number theory problems taken mainly from mathematical olympiads and other contests held in different countries, mainly in recent years. … This makes the book a useful source of material for tests, homeworks, projects, and classroom discussion. … Number Theory Problems Amir Hossein Parvardi ∗ June 16, 2011 I’ve written the source of the problems beside their numbers. If you need solutions, visit AoPS Resources Page, select the competition, select the year and go to the link of the problem.

Number Theory. Camsie's New Job. Here are some of our favorite countdown round problems from the 2019 competitions. School #16 On a certain farm, each chicken has two feet and each rabbit has four feet. If the combined number of chickens and rabbits on the farm is 100 and there are a total of 260 feet on these animals, how many chickens are Amazon.in - Buy Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad Series) book online at best prices in India on Amazon.in. Read Problems of Number Theory in Mathematical Competitions (Mathematical Olympiad Series) book reviews & author details and more at Amazon.in. Free delivery on qualified orders.

2. Read the problems through again and make notes on the six problems: (a) What category of math: calculus, linear algebra, number theory, etc. (b) Underline the data in each problem (c) Estimate the di culty and devise an order of attack. While A-1 and B-1 are usually the easiest in each session, that may not be the case for a given year and Mathematics is the queen of sciences and arithmetic the queen of mathematics.” At first blush one might think that of all areas of mathematics certainly arithmetic should be the simplest, but it is a surprisingly deep subject. We assume that students have some familiarity with basic set theory…

Number theory is an important research field of mathematics. In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. They are flexible and diverse. In this book, the author introduces some basic concepts and methods in elementary number theory via The heart of Mathematics is its problems. Paul Halmos 1. Introduction Number Theory is a beautiful branch of Mathematics. The purpose of this book is to present a collection of interesting questions in Number Theory. Many of the problems are mathematical competition problems all over the world including IMO, APMO, APMC, and Putnam, etc.

problems of number theory in mathematical competitions pdf

Sep 22, 2013В В· Competition problems Problem (2003 AIME II, Problem 2.) Find the greatest integer multiple of 8, no two of whose digits are the same. Problem (2009 PUMaC Number Theory, Problem A1.) If 17! = 355687ab8096000, where a and b are two missing digits, nd a and b. Problem (2004 AIME II, Problem 10.) Number Theory - Modular arithmetic and GCD PROBLEMS IN ELEMENTARY NUMBER THEORY 5 2.2. Sources. 1. 1969 EВЁotvВЁos-KurschВґВЁ ak Mathematics Competition 2. IMO 1988/6 3. 4. Turkey 1994 5. Mediterranean Mathematics Competition 2002 6. IMO 1998/4 7. Unused Problem for the Balkan Mathematical Olympiad

Like
Like Love Haha Wow Sad Angry
477692