An infinite collection of quartic polynomials whose products of consecutive values are not perfect squares

Konstantinos Gaitanas

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arXiv · 1610.02340

An infinite collection of quartic polynomials whose products of consecutive values are not perfect squares

Konstantinos Gaitanas

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Abstract

Using an elementary identity, we prove that for infinitely many polynomials $P(x)\in \mathbb{Z}[X]$ of fourth degree, the equation $\prod\limits_{k=1}^{n}P(k)=y^2$ has finitely many solutions in $\mathbb{Z}$. We also give an example of a quartic polynomial for which the product of it's first consecutive values is infinitely often a perfect square.

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Konstantinos Gaitanas. 2016-10-04. An infinite collection of quartic polynomials whose products of consecutive values are not perfect squares. https://arxiv.org/abs/1610.02340

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