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Prove that a=1 if 4(a^n+1) is a cube for all n (Iran 2008)

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September 22, 2010
number theory proposednumber theory

Problem Statement

N\mathbb{N} is the set of positive integers and a∈Na\in\mathbb{N}. We know that for every n∈Nn\in\mathbb{N}, 4(an+1)4(a^n+1) is a perfect cube. Prove that a=1a=1.
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