Some new results on negative polynomial Pell's equation

2021/01/13 by K. Anitha, Anitha, K., I. Mumtaj Fathima +3
Mathematics · #11A99 #11C08 #11D99 #Advanced Differential Equations and Dynamical Systems #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2101.04906

openalex publication_date 2021/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the negative polynomial Pell's equation P²(X)-D(X)Q²(X)=-1, where D(X)∈ 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.

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