Two-parameter families of uniquely extendable Diophantine triples |
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| Authors: | Mihai Cipu Yasutsugu Fujita Maurice Mignotte |
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| Institution: | 1.Simion Stoilow Institute of Mathematics of the Romanian Academy,Bucharest,Romania;2.Department of Mathematics, College of Industrial Technology,Nihon University,Chiba,Japan;3.Département de Mathématique,Université de Strasbourg,Strasbourg,France |
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| Abstract: | Let A and K be positive integers and ? ∈ {?2;?1, 1, 2}. The main contribution of the paper is a proof that each of the D(?2)-triples {K,A2K + 2?A, (A + 1)2K + 2?(A + 1)} has unique extension to a D(?2)- quadruple. This is used to slightly strengthen the conditions required for the existence of a D(1)-quintuple whose smallest three elements form a regular triple. |
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