Open Access
november 2013 On the family of $D(4)$-triples {k-2, k+2, 4k^3-4k}
Ljubica Baćić, Alan Filipin
Bull. Belg. Math. Soc. Simon Stevin 20(5): 777-787 (november 2013). DOI: 10.36045/bbms/1385390763


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 $d=4k^5-12k^3+8k$.


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Ljubica Baćić. Alan Filipin. "On the family of $D(4)$-triples {k-2, k+2, 4k^3-4k}." Bull. Belg. Math. Soc. Simon Stevin 20 (5) 777 - 787, november 2013.


Published: november 2013
First available in Project Euclid: 25 November 2013

zbMATH: 1323.11018
MathSciNet: MR3160588
Digital Object Identifier: 10.36045/bbms/1385390763

Primary: 11D09
Secondary: 11J86

Keywords: Diophantine tuples , system of Diophantine equations

Rights: Copyright © 2013 The Belgian Mathematical Society

Vol.20 • No. 5 • november 2013
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