Difference between revisions of "2022 USAJMO Problems/Problem 1"
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Revision as of 21:28, 19 April 2022
We claim that satisfies the given conditions if and only if is squareful.
To begin, we let the common difference be and the common ratio be . Then, rewriting the conditions modulo gives:
Condition holds iff no consecutive terms in are equivalent modulo , which is the same thing as never having consecutive, equal, terms, in . By Condition , this is also the same as never having equal, consecutive, terms in :
Also, Condition holds iff
Whee! Restating, , and the conditions and hold if and only if is not squareful.
[will finish that step here]