Cube sum problem for integers having exactly two distinct prime factors

Dipramit Majumdar; Pratiksha Shingavekar

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arXiv · 2211.17118

Cube sum problem for integers having exactly two distinct prime factors

Dipramit Majumdar·Pratiksha Shingavekar

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Abstract

Given an integer n>1, it is a classical Diophantine problem that whether n can be written as a sum of two rational cubes. The study of this problem, considering several special cases of n, has a copious history that can be traced back to the works of Sylvester, Satg\'e, Selmer etc. and up to the recent works of Alp\"oge-Bhargava-Shnidman. In this article, we consider the cube sum problem for cube-free integers n which has two distinct prime factors none of which is 3.

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Dipramit Majumdar, Pratiksha Shingavekar. 2022-11-30. Cube sum problem for integers having exactly two distinct prime factors. https://arxiv.org/abs/2211.17118

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