Some new results on negative polynomial Pell's equation

Abstract

We consider the negative polynomial Pell's equation $P^2(X)-D(X)Q^2(X)=-1$, where $D(X)\in \mathbb{Z}[X]$ be some fixed, monic, square-free, even degree polynomials. In this paper, we investigate the existence of polynomial solutions $P(X),Q(X)$ with integer coefficients.

10 pages, some more equations added

References in corpus (1)

• Higher Rédei reciprocity and integral points on conics