Fruit Diophantine Equation

• Published in 2021
• Added on 2021-08-29

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.

Links

• http://arxiv.org/abs/2108.02640v2
• http://arxiv.org/pdf/2108.02640v2

Other information

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}
}