BINARY CUBIC FORMS AND RATIONAL CUBE SUM PROBLEM

Authors

• Somnath Jha, Indian Institute of Technology Kanpur
• Dipramit Majumdar, Indian Institute of Technology Madras
• B. Sury, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Proceedings of the American Mathematical Society

Abstract

In this note, we use binary cubic forms to study the rational cube sum problem. We prove that every non-zero residue class a (mod q), for any prime q, contains infinitely many primes which are sums of two rational cubes. We also prove (unconditionally) that for any positive integer d, infinitely many primes in each of the residue classes 1 (mod 9d) as well as −1 (mod 9d) are sums of two rational cubes. Further, for an arbitrary integer N, we show there are infinitely many primes p in each of the residue classes 8 (mod 9) and 1 (mod 9), such that Np is a sum of two rational cubes.

First Page

4657

Last Page

4668

DOI

10.1090/proc/17366

Publication Date

11-1-2025

Recommended Citation

Jha, Somnath; Majumdar, Dipramit; and Sury, B., "BINARY CUBIC FORMS AND RATIONAL CUBE SUM PROBLEM" (2025). Journal Articles. 5259.
https://digitalcommons.isical.ac.in/journal-articles/5259