English

Cube sum problem for integers having exactly two distinct prime factors

Number Theory 2022-12-01 v1

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.

Keywords

Cite

@article{arxiv.2211.17118,
  title  = {Cube sum problem for integers having exactly two distinct prime factors},
  author = {Dipramit Majumdar and Pratiksha Shingavekar},
  journal= {arXiv preprint arXiv:2211.17118},
  year   = {2022}
}

Comments

15 pages

R2 v1 2026-06-28T07:18:20.175Z