ISL 2009 N7

Number theory
Difficulty band 8

Let $a$ and $b$ be distinct integers greater than 1 . Prove that there exists a positive integer $n$ such that $\left(a^{n}-1\right)\left(b^{n}-1\right)$ is not a perfect square.

Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.

Official text: IMO 2009 Shortlist booklet, page 13.

Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

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