On the size of Diophantine m-tuples
Andrej Dujella
Abstract
Let n be a nonzero integer and assume that a set S of positive integers has the property that xy+n is a perfect square whenever x and y are distinct elements of S. In this paper we find some upper bounds for the size of the set S. We prove that if |n| <= 400 then |S| <= 32, and if |n| > 400 then |S| < 267.81 log|n| (log log|n|)2. The question whether there exists an absolute bound (independent on n) for |S| still remains open.
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