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  • 1 Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan
  • 2 Mathematics Department, Purdue University North Central, 1401 S, U.S. 421, Westville, IN 46391, USA
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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].

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