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a^+b^n-c^n

Source: Iran 2005

August 29, 2005
inductionnumber theoryprime numbersnumber theory proposed

Problem Statement

Let a,b,c∈Na,b,c\in \mathbb N be such that a,b≠ca,b\neq c. Prove that there are infinitely many prime numbers pp for which there exists n∈Nn\in\mathbb N that p∣an+bn−cnp|a^n+b^n-c^n.
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