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

2016/08/31 by Yong Zhang
Mathematics · #math.NT

paper · pdf

published as Colloquium Mathematicum, 151 (2018), 111--122 · 10 pages. Any comments are welcome. arXiv admin note: text overlap with arXiv:1608.03810

arxiv created 2018/02/04 · arxiv updated 2018/02/06

Abstract

By the theory of elliptic curves, we investigate the nontrivial rational parametric solutions of the Diophantine equation f(x)f(y)=f(z)ⁿ, where n=1,2 and f(X) are some simple Laurent polynomials.

Citations

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

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