engleski

Strong Diophantine triples

We prove that there exist infinitely many triples a, b, c of non-zero rationals with the property that a^2+1, b^2+1, c^2+1, ab+1, ac+1 and bc+1 are perfect squares. Using some elliptic curves over Q with positive rank, we give two different constructions of such triples.

Diophantine triples

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