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Strong Diophantine triples. (English) Zbl 1218.11029

Summary: 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.

MSC:

11D09 Quadratic and bilinear Diophantine equations
11G05 Elliptic curves over global fields
11Y50 Computer solution of Diophantine equations
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