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Lifting the Exponent

Revision as of 21:12, 19 June 2024 by Ab godder (talk | contribs)
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(Lemma from MAA official solution, 2020 AIME I Problems/Problem 12)

Denote $v_p(n)$ the highest power of prime $p$ that divides $n$. Let $p$ be an odd prime, and let $a$ and $b$ be integers that are not multiples of $p$ such that $p \mid (a-b)$. Let $n$ be a positive integer. Then $v_p(a^n - b^n) = v_p(a - b) + v_p(n)$.

For more conclusions, see https://en.wikipedia.org/wiki/Lifting-the-exponent_lemma

edit by ~ab_godder

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