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Displaying similar documents to “Linear polynomials in numbers of bounded degree”

Some observations on the Diophantine equation f(x)f(y) = f(z)²

Yong Zhang (2016)

Colloquium Mathematicae

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Let f ∈ ℚ [X] be a polynomial without multiple roots and with deg(f) ≥ 2. We give conditions for f(X) = AX² + BX + C such that the Diophantine equation f(x)f(y) = f(z)² has infinitely many nontrivial integer solutions and prove that this equation has a rational parametric solution for infinitely many irreducible cubic polynomials. Moreover, we consider f(x)f(y) = f(z)² for quartic polynomials.