2022 USAJMO Problems
Contents
[hide]Day 1
For any geometry problem whose statement begins with an asterisk , the first page of the solution must be a large, in-scale, clearly labeled diagram. Failure to meet this requirement will result in an automatic 1-point deduction.
Problem 1
For which positive integers does there exist an infinite arithmetic sequence of integers and an infinite geometric sequence of integers satisfying the following properties?
is divisible by for all integers ;
is not divisible by .
Problem 2
Let and be positive integers. The cells of an grid are colored amber and bronze such that there are at least $a^2 + ab − b$ (Error compiling LaTeX. Unknown error_msg) amber cells and at least $b^2 + ab − a$ (Error compiling LaTeX. Unknown error_msg) bronze cells. Prove that it is possible to choose amber cells and bronze cells such that no two of the chosen cells lie in the same row or column.
Problem 3
Day 2
Problem 4
Problem 5
Problem 6
2021 USAJMO (Problems • Resources) | ||
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Followed by 2023 USAJMO | |
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The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.