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2022 SSMO Accuracy Round Problems/Problem 5

Revision as of 13:03, 14 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Find the number of ordered pairs <math>(a, b)</math>, where <math>1\leq a, b\leq 9</math>, for which the largest integer <math>n</math> that satisfies<cmath>(a-b)^...")
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Problem

Find the number of ordered pairs $(a, b)$, where $1\leq a, b\leq 9$, for which the largest integer $n$ that satisfies\[(a-b)^k\equiv a^k-b^k\pmod n\]for all $k\geq 1$ is $ab-b^2$.

Solution

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