Experimental Mathematics

Strong Diophantine Triples

Andrej Dujella and Vinko Petričcević

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Abstract

We prove that there exist infinitely many triples $a,b,c$ of nonzero rational numbers with the property that $a^2+1$, $b^2+1$, $c^2+1$, $ab+1$, $ac+1$, and $bc+1$ are perfect squares.

Article information

Source
Experiment. Math., Volume 17, Issue 1 (2008), 83-89.

Dates
First available in Project Euclid: 18 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.em/1227031899

Mathematical Reviews number (MathSciNet)
MR2410118

Zentralblatt MATH identifier
1218.11029

Subjects
Primary: 11D09: Quadratic and bilinear equations
Secondary: 11G05: Elliptic curves over global fields [See also 14H52] 11Y50: Computer solution of Diophantine equations

Keywords
Diophantine triples elliptic curves

Citation

Dujella, Andrej; Petričcević, Vinko. Strong Diophantine Triples. Experiment. Math. 17 (2008), no. 1, 83--89. https://projecteuclid.org/euclid.em/1227031899


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