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

2016/08/11 by Yong Zhang, Zhang, Yong, Arman Shamsi Zargar +1 · 2 citations
Mathematics · Physics and Astronomy · #11D25 #11G05 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT) #Primary 11D72 #Secondary 11D41 #math.NT #msc:11D25 #msc:11D41 #msc:11D72 #msc:11G05

paper · pdf · doi:10.48550/arxiv.1608.03810

8 pages. Submitted for publication. Any comments are welcome. arXiv admin note: text overlap with arXiv:1608.03809

openalex publication_date 2016/08/11 · openalex created_date 2016/09/16 · arxiv created 2018/02/04 · arxiv updated 2018/02/06 · 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 ± f(y)² for some simple Laurent polynomials f.

Citations

• On the Diophantine equation f(x)f(y)=f(z)ⁿ involving Laurent polynomials

Cited by

• On the Diophantine equation f(x)f(y)=f(z)ⁿ involving Laurent polynomials
• On the Diophantine equations z²=f(x)² ± g(y)² concerning Laurent polynomials

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