Interesting Esoterica

Fruit Diophantine Equation

Article by Dipramit Majumdar and B. Sury
  • Published in 2021
  • Added on
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}
}