MathDB
Ibero American 2012 - Problem 4

Source:

October 3, 2012
inductionmodular arithmeticstrong inductionalgebra proposedalgebra

Problem Statement

Let a,b,c,da,b,c,d be integers such that the number a−b+c−da-b+c-d is odd and it divides the number a2−b2+c2−d2a^2-b^2+c^2-d^2. Show that, for every positive integer nn, a−b+c−da-b+c-d divides an−bn+cn−dna^n-b^n+c^n-d^n.
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