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Difference between revisions of "2022 USAJMO Problems"

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| style="background:#ccf;text-align:center;" colspan="3" | '''[[2021 USAJMO]]''' ('''[[2021 USAJMO Problems|Problems]]''' • [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=176&year={{{year}}} Resources])
 
| style="background:#ccf;text-align:center;" colspan="3" | '''[[2021 USAJMO]]''' ('''[[2021 USAJMO Problems|Problems]]''' • [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=176&year={{{year}}} Resources])
 
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| colspan="3" style="text-align:center;" | [[2021 USAJMO Problems/Problem 1|1]] '''•''' [[2021 USAJMO Problems/Problem 2|2]] '''•''' [[2021 USAJMO Problems/Problem 3|3]] '''•''' [[2021 USAJMO Problems/Problem 4|4]] '''•''' [[2021 USAJMO Problems/Problem 5|5]] '''•''' [[2021 USAJMO Problems/Problem 6|6]]
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| colspan="3" style="text-align:center;" | [[2021 USAJMO Problems/Problem 1|1]] '''•''' [[2021 USAJMO Problems/Problem 2|2]] '''•''' [[2022 USAJMO Problems/Problem 3|3]] '''•''' [[2022 USAJMO Problems/Problem 4|4]] '''•''' [[2022 USAJMO Problems/Problem 5|5]] '''•''' [[2021 USAJMO Problems/Problem 2|6]]
 
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| colspan="3" style="text-align:center;" | '''[[USAJMO Problems and Solutions | All USAJMO Problems and Solutions]]'''
 
| colspan="3" style="text-align:center;" | '''[[USAJMO Problems and Solutions | All USAJMO Problems and Solutions]]'''

Revision as of 21:06, 19 April 2022

Day 1

$\textbf{Note:}$ 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 $m$ does there exist an infinite arithmetic sequence of integers $a_1,a_2,\cdots$ and an infinite geometric sequence of integers $g_1,g_2,\cdots$ satisfying the following properties?

[-] $a_n-g_n$ is divisible by $m$ for all integers $n>1$;

[-] $a_2-a_1$ is not divisible by $m$.

Problem 2

Solution

Problem 3

Solution

Day 2

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

2021 USAJMO (Problems • Resources)
Preceded by
2021 USAJMO 		Followed by
2023 USAJMO
1 • 2 • 3 • 4 • 5 • 6
All USAJMO Problems and Solutions

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