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The Extensibility of the Diophantine Triple {;2,b,c};

The aim of this paper is to consider the extensibility of the Diophantine triple {;2, b, c}; and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of c's (depending on b). As corollary, for example, we prove that for b/2-1 prime, all Diophantine quadruples {;2, b, c, d}; are regular.

Diophantine tuples, system of Pellian equations, linear forms in logarithms

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