Difference between revisions of "Lifting the Exponent"

Latest revision as of 19:50, 10 March 2025

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-(Lemma from MAA official solution, 2020 AIME I Problems/Problem 12)
+#redirect [[Lifting the Exponent Lemma]]
-Denote <math>v_p(n)</math> the highest power of prime <math>p</math> that divides <math>n</math>.
-Let <math>p</math> be an odd prime, and let <math>a</math> and <math>b</math> be integers that are not multiples of <math>p</math> such that <math>p \mid (a-b)</math>. Let <math>n</math> be a positive integer. Then <math>v_p(a^n - b^n) = v_p(a - b) + v_p(n)</math>.
-For more conclusions, see https://en.wikipedia.org/wiki/Lifting-the-exponent_lemma
-edit by ~ab_godder