Two-parameter families of uniquely extendable Diophantine triples

Mihai Cipu; Yasutsugu Fujita; Maurice Mignotte

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arXiv · 1611.08646

Two-parameter families of uniquely extendable Diophantine triples

Mihai Cipu·Yasutsugu Fujita·Maurice Mignotte

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Abstract

Let A,K be positive integers and u=-2,-1,1 or 2. The main contribution of the paper is a proof that each of the D(u^2)-triples {K,A^2K+2uA,(A+1)^2K+2u(A+1)} has unique extension to a D(u^2)-quadruple.

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Mihai Cipu, Yasutsugu Fujita, Maurice Mignotte. 2016-11-26. Two-parameter families of uniquely extendable Diophantine triples. https://arxiv.org/abs/1611.08646

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