Periodica Mathematica Hungarica

, Volume 65, Issue 1, pp 75–81

# The extension of the D(−k2)-pair {k2,k2 + 1}

Article

## Abstract

Let n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the product of any two of them increased by n is a perfect square. Let k be a positive integer. In this paper, we show that if {k 2, k 2+1, c, d} is a D(−k 2)-quadruple with c < d, then c = 1 and d = 4k 2+1. This extends the work of the first author [20] and that of Dujella [4].

## Key words and phrases

Diophantine tuples simultaneous Diophantine equations

11D09 11J68

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