On the Diophantine equation $f(x)=2f(y)$

Abstract

Let $f(x)=x^2(x^2-1)(x^2-2)(x^2-3).$ We prove that the Diophantine equation $f(x)=2f(y)$ has no solutions in positive integers $x$ and $y$, except $(x,y)=(1,1)$.

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