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Integer partitions into Diophantine pairs. (English) Zbl 1423.05020

Summary: Let \(n, a\) and \(b\) be positive integers. The pair \((a,b)\) is called \(an\) integer partition of \(n\) into Diophantine pair if \(n=a+b\), \(ab+1\) is a perfect square and \(a > b\). In this paper we give, for any positive integer \(n\), a closed formula for the number of integer partitions into Diophantine pairs.

MSC:

05A17 Combinatorial aspects of partitions of integers
11P83 Partitions; congruences and congruential restrictions
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References:

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