Two-parameter families of uniquely extendable Diophantine triples

Mihai Cipu, Yasutsugu Fujita, Maurice Mignotte

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…