Difference between revisions of "2022 USAJMO Problems"
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For which positive integers <math>m</math> does there exist an infinite arithmetic sequence of integers <math>a_1,a_2,\cdots</math> and an infinite geometric sequence of integers <math>g_1,g_2,\cdots</math> satisfying the following properties? | For which positive integers <math>m</math> does there exist an infinite arithmetic sequence of integers <math>a_1,a_2,\cdots</math> and an infinite geometric sequence of integers <math>g_1,g_2,\cdots</math> satisfying the following properties? | ||
| − | + | <math>\bullet</math> <math>a_n-g_n</math> is divisible by <math>m</math> for all integers <math>n>1</math>; | |
| − | + | <math>\bullet</math> <math>a_2-a_1</math> is not divisible by <math>m</math>. | |
===Problem 2=== | ===Problem 2=== | ||
Revision as of 21:06, 19 April 2022
Contents
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
Problem 3
Day 2
Problem 4
Problem 5
Problem 6
| 2021 USAJMO (Problems • Resources) | ||
| Preceded by 2021 USAJMO |
Followed by 2023 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. 
