2015/01/19 by Tim Trudgian, Trudgian, Tim
Mathematics · #11D45 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D45
paper · pdf · doi:10.48550/arxiv.1501.04401
16 pages
arxiv created 2015/01/19 · arxiv updated 2015/01/20
We consider Diophantine quintuples \a, b, c, d, e\. These are sets of distinct 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 1.9⋅ 1029 Diophantine quintuples.