Affiliation:
1. Faculty of Civil Engineering , University of Zagreb , Fra Andrije Kačića-Miošića 26, 10000 Zagreb , Croatia
2. Department of Mathematics , University of Rijeka , Radmile Matejčić 2, 51000 Rijeka , Croatia
Abstract
Abstract
The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 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} with 2 < b < c < d are regular.
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