Published January 1, 2024 | Version v1
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An elementary approach to the generalized Ramanujan-Nagell equation

  • 1. Bursa Uludag Univ, Dept Math, TR-16059 Bursa, Turkiye
  • 2. Lingnan Normal Coll, Inst Math, Zhanjiang 524048, Guangdong, Peoples R China

Description

Let k be a fixed positive integer with k > 1. In this paper, using various elementary methods in number theory, we give criteria under which the equation x(2) + (2k - 1)(y) = k(z) has no positive integer solutions (x, y, z) with y is an element of {3, 5}.

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