# Fruit Diophantine Equation

- Published in 2021
- Added on

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.

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## Other information

- key
- FruitDiophantineEquation
- type
- article
- date_added
- 2021-08-29
- date_published
- 2021-10-09

### BibTeX entry

@article{FruitDiophantineEquation, key = {FruitDiophantineEquation}, type = {article}, title = {Fruit Diophantine Equation}, author = {Dipramit Majumdar and B. Sury}, 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.}, comment = {}, date_added = {2021-08-29}, date_published = {2021-10-09}, urls = {http://arxiv.org/abs/2108.02640v2,http://arxiv.org/pdf/2108.02640v2}, collections = {attention-grabbing-titles,easily-explained,food,integerology}, url = {http://arxiv.org/abs/2108.02640v2 http://arxiv.org/pdf/2108.02640v2}, year = 2021, urldate = {2021-08-29}, archivePrefix = {arXiv}, eprint = {2108.02640}, primaryClass = {math.NT} }