Let and be distinct integers greater than . Prove that there exists a positive integer such that is not a perfect square.
Proposed by Mongolia
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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.
Proposed by Mongolia
Izvor: Međunarodna matematička olimpijada, shortlist 2009
Školjka 
and 
be distinct integers greater than 
. Prove that there exists a positive integer 
such that 
is not a perfect square.