English

Fruit Diophantine Equation

History and Overview 2021-11-15 v2 Number Theory

Abstract

We show that the Diophantine equation given by X^3+ XYZ = Y^2+Z^2+5 has no integral solution. As a consequence, we show that the family of elliptic curve given by the Weierstrass equations Y^2-kXY = X^3 - (k^2+5) has no integral point.

Keywords

Cite

@article{arxiv.2108.02640,
  title  = {Fruit Diophantine Equation},
  author = {Dipramit Majumdar and B. Sury},
  journal= {arXiv preprint arXiv:2108.02640},
  year   = {2021}
}

Comments

3 pages, couple of typos fixed

R2 v1 2026-06-24T04:51:41.873Z