Bounds for the size of sets with the property D(n)

Abstract

Let n be a nonzero integer and a_1 < a_2 < ... <a_m positive integers such that a_i*a_j + n is a perfect square for all 1 <= i < j <= m. It is known that m <= 5 for n = 1. In this paper we prove that m <= 31 for |n| <= 400 and m < 15.476 log|n| for |n| > 400.

9 pages. Revised - removed a gap in the proof of Proposition 1; to appear in Glasnik Matematicki

References in corpus (1)

• On the size of Diophantine m-tuples

Cited by in corpus (9)

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• Triples which are $D(n)$-sets for several $n$'s
• Diophantine quadruples with the properties $D(n_1)$ and $D(n_2)$
• A Polynomial Variant of Diophantine Triples in Linear Recurrences
• Explicit constructions of Diophantine tuples over finite fields
• On the largest element in D(n)-quadruples
• Improved upper bounds on Diophantine tuples with the property $D(n)$
• The extension of the $D(-k)$-pair $\{k,k+1\}$ to a quadruple
• A polynomial variant of a problem of Diophantus and its consequences