Bulletin of the Belgian Mathematical Society - Simon Stevin

On the family of $D(4)$-triples {k-2, k+2, 4k^3-4k}

Ljubica Baćić and Alan Filipin

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Abstract

In this paper we prove that if $k\geq3$ and $d$ are positive integers and the set $\{k-2,k+2,4k^3-4k,d\}$ has the property that the product of any two of its distinct elements increased by $4$ is a perfect square, then $d=4k$ or $d=4k^5-12k^3+8k$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 5 (2013), 777-787.

Dates
First available in Project Euclid: 25 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1385390763

Digital Object Identifier
doi:10.36045/bbms/1385390763

Mathematical Reviews number (MathSciNet)
MR3160588

Zentralblatt MATH identifier
1323.11018

Subjects
Primary: 11D09: Quadratic and bilinear equations
Secondary: 11J86: Linear forms in logarithms; Baker's method

Keywords
Diophantine tuples system of Diophantine equations

Citation

Baćić, Ljubica; Filipin, Alan. On the family of $D(4)$-triples {k-2, k+2, 4k^3-4k}. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 5, 777--787. doi:10.36045/bbms/1385390763. https://projecteuclid.org/euclid.bbms/1385390763


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