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The extension of the D(−k 2)-pair {k 2,k 2 + 1}

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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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Authors and Affiliations

  1. Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan

    Yasutsugu Fujita

  2. Mathematics Department, Purdue University North Central, 1401 S, U.S. 421, Westville, IN, 46391, USA

    Alain Togbé

Authors
  1. Yasutsugu Fujita
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  2. Alain Togbé
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Correspondence to Yasutsugu Fujita.

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Communicated by Attila Pethő

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Fujita, Y., Togbé, A. The extension of the D(−k 2)-pair {k 2,k 2 + 1}. Period Math Hung 65, 75–81 (2012). https://doi.org/10.1007/s10998-012-2912-x

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  • DOI: https://doi.org/10.1007/s10998-012-2912-x

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