On symmetric square values of quadratic polynomials

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.

Cited by in corpus (2)

• On a conjecture of Rudin on squares in Arithmetic Progressions
• Quadratic sequences of powers and Mohanty's Conjecture