Diophantine quintuples containing triples of the first kind |
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| Authors: | David J. Platt Timothy S. Trudgian |
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| Affiliation: | 1.Heilbronn Institute for Mathematical Research,University of Bristol,Bristol,UK;2.Mathematical Sciences Institute,The Australian National University,Canberra,Australia |
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| Abstract: | We consider Diophantine quintuples ({a, b, c, d, e}), sets of integers with (a the product of any two elements of which is one less than a perfect square. Triples of the first kind are sets ({A, B, C}) with (Cge B^{5}). We show that there are no Diophantine quintuples ({a, b, c, d, e}) such that ({a, b, d}) is a triple of the first kind. |
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