# Fruit Diophantine Equation

- Published in 2021
- Added on

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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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### 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} }