On symmetric square values of quadratic polynomials
Number Theory
2014-11-12 v1 Algebraic Geometry
Abstract
We prove that there does not exist a non-square quadratic polynomial with integer coefficients and an axis of symmetry which takes square values for N consecutive integers for N=7 or N >= 9. At the opposite, if N <= 6 or N=8 there are infinitely many.
Keywords
Cite
@article{arxiv.1001.4710,
title = {On symmetric square values of quadratic polynomials},
author = {Enrique Gonzalez-Jimenez and Xavier Xarles},
journal= {arXiv preprint arXiv:1001.4710},
year = {2014}
}