# Fruit Diophantine Equation

• Published in 2021
In the collections
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.

### BibTeX entry

@article{FruitDiophantineEquation,
title = {Fruit Diophantine Equation},
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.},
url = {http://arxiv.org/abs/2108.02640v2 http://arxiv.org/pdf/2108.02640v2},
year = 2021,
author = {Dipramit Majumdar and B. Sury},
comment = {},
urldate = {2021-08-29},
archivePrefix = {arXiv},
eprint = {2108.02640},
primaryClass = {math.NT},
collections = {attention-grabbing-titles,easily-explained,food,integerology}
}