Infinite families of solutions for A3 + B3 = C3 + D3 and A4 + B4 + C4 + D4 + E4 = F4 in the spirit of Ramanujan

IF 0.5 3区数学 Q3 MATHEMATICS

International Journal of Number Theory Pub Date : 2023-11-02 DOI:10.1142/s1793042124500283

Archit Agarwal, Meghali Garg

引用次数: 0

Abstract

Ramanujan, in his lost notebook, gave an interesting identity, which generates infinite families of solutions to Euler’s Diophantine equation [Formula: see text]. In this paper, we produce a few infinite families of solutions to the aforementioned Diophantine equation as well as for the Diophantine equation [Formula: see text] in the spirit of Ramanujan.

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以拉马努扬精神为基础的 A3 + B3 = C3 + D3 和 A4 + B4 + C4 + D4 + E4 = F4 的无穷解族

拉马努金在他丢失的笔记本中给出了一个有趣的恒等式，它可以生成欧拉丢芬图方程的无穷族解[公式:见原文]。在本文中，我们本着拉马努金的精神，对上述丢番图方程和丢番图方程[公式:见文]给出了几个无穷族的解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.