Searching for Diophantine quintuples
Date
2016-05-18
Authors
Cipu, Mihai
Trudgian, Tim
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Publisher
Polish Academy of Sciences, Institute of Mathematics
Abstract
We consider Diophantine quintuples {a,b,c,d,e}. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most 5.441⋅10²⁶ Diophantine quintuples.
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Keywords
Diophantine m-tuples, Pell equations, linear forms in logarithms
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Source
Acta Arithmetica
Type
Journal article
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Open Access
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