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USAJMO 2022 Question 1

USAJMO · USAJMO 2022

Question 1

For which positive integers $m$ does there exist an infinite sequence in $\mathbb Z/m\mathbb Z$ which is both an arithmetic progression and a geometric progression, but is nonconstant?

Proposed by Holden Mui. Source: Evan Chen’s third-party compilation; https://aops.com/community/p24774800. One editorial point; manual grading.