2022 USAJMO Problems

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

Solution 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

Solution

Problem 3

Solution

Day 2

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

2021 USAJMO (Problems • Resources)
Preceded by 2020 USOJMO	Followed by 2022 USAJMO
1 • 2 • 3 • 4 • 5 • 6
All USAJMO Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.