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Let \(p\) be a prime. A Prime Pellian Triangle for prime \(p\) or \(p\) - Pellian triangle is an isosceles triangle with sides \(x,x,y\) or \(x,y,y\) such that \(x^{2} - py^{2} = 1\) where \(x,y \in {\mathbb{R}}\) and \(x^{2} ,y^{2} \in {\mathbb{Z}}\) . In this paper, employing the concepts such as congruence and recurrence relations, we aim to collect all Prime Pellian triangles with sides \(x,x,y\) and having area as a rational number for the even prime and odd primes satisfying \(p \equiv 3 \left( {mod 4} \right)\) .

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A Mobilization of p- Pellian Triangles with Area in \({\mathbb{Q}}\)

  • 会议论文

  • 发表日期：

    2025年

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  • J. Kannan,
  • M. Mahalakshmi,
  • K. Kaleeswari

摘要

Let \(p\) be a prime. A Prime Pellian Triangle for prime \(p\) or \(p\) - Pellian triangle is an isosceles triangle with sides \(x,x,y\) or \(x,y,y\) such that \(x^{2} - py^{2} = 1\) where \(x,y \in {\mathbb{R}}\) and \(x^{2} ,y^{2} \in {\mathbb{Z}}\) . In this paper, employing the concepts such as congruence and recurrence relations, we aim to collect all Prime Pellian triangles with sides \(x,x,y\) and having area as a rational number for the even prime and odd primes satisfying \(p \equiv 3 \left( {mod 4} \right)\) .