Difference between revisions of "2022 USAJMO Problems"
Aidensharp (talk | contribs) |
(→Problem 1) |
||
| Line 5: | Line 5: | ||
[[2022 USAJMO Problems/Problem 1|Solution]] | [[2022 USAJMO Problems/Problem 1|Solution]] | ||
| + | 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>a_n-g_n</math> is divisible by <math>m</math> for all integers <math>n>1</math>; | ||
| + | |||
| + | [-] <math>a_2-a_1</math> is not divisible by <math>m</math>. | ||
| + | |||
===Problem 2=== | ===Problem 2=== | ||
Revision as of 20:05, 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 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. 
