Bulletin of the Belgian Mathematical Society - Simon Stevin

On a Diophantine Equation of Stroeker

Florian Luca, Pantelimon Stănică, and Alain Togbé

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Abstract

In this paper, we prove that there are infinitely many positive integers $N$ such that the Diophantine equation $(x^2+y)(x+y^2)=N(x-y)^3$ has no nontrivial integer solution $(x,y)$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 2 (2010), 201-208.

Dates
First available in Project Euclid: 26 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1274896199

Digital Object Identifier
doi:10.36045/bbms/1274896199

Mathematical Reviews number (MathSciNet)
MR2663465

Zentralblatt MATH identifier
1205.11038

Subjects
Primary: 11D25: Cubic and quartic equations 11G05: Elliptic curves over global fields [See also 14H52]

Keywords
Diophantine equations Elliptic Curves

Citation

Luca, Florian; Stănică, Pantelimon; Togbé, Alain. On a Diophantine Equation of Stroeker. Bull. Belg. Math. Soc. Simon Stevin 17 (2010), no. 2, 201--208. doi:10.36045/bbms/1274896199. https://projecteuclid.org/euclid.bbms/1274896199


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