Difference between revisions of "Lifting the Exponent"

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−	(Lemma ~~from MAA official solution, 2020 AIME I Problems/Problem 12)~~	+	#redirect [[Lifting the Exponent Lemma]]
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−	Let <math>p</math> be an odd prime, and let <math>a</math> and <math>b</math> be integers relatively prime to <math>p</math> such that <math>p \mid (a-b)</math>. Let <math>n</math> be a positive integer. Then the number of factors of <math>p</math> that divide <math>a^n - b^n</math> is equal to the number of factors of <math>p</math> that divide <math>a-b</math> plus the number of factors of <math>p</math> that divide <math>n</math>.