Abstract
We show that the Diophantine system $$\begin{aligned} f(z)=f(x)f(y)=f(u)f(v) \end{aligned}$$ has infinitely many nontrivial positive integer solutions for \(f(X)=X^2-1\), and infinitely many nontrivial rational solutions for \(f(X)=X^2+b\) with nonzero integer b.
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