On the Diophantine equations z²=f(x)² ± g(y)² concerning Laurent polynomials

2017/06/08 by Yong Zhang, Zhang, Yong, Arman Shamsi Zargar +1
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1706.02925

7 pages. Submitted for publication. arXiv admin note: substantial text overlap with arXiv:1608.03810

arxiv created 2017/06/08 · openalex publication_date 2017/06/08 · arxiv updated 2017/06/12 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

By the theory of elliptic curves, we study the nontrivial rational parametric solutions and rational solutions of the Diophantine equations z²=f(x)² ± g(y)² for some simple Laurent polynomials f and g.

Citations

• On the Diophantine equations z²=f(x)² ± f(y)² involving Laurent polynomials

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