On Pythagorean triplet semigroups

Antoine Mhanna
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310-5132, Online ISSN 2367-8275
Volume 26, 2020, Number 4, Pages 63—67
DOI: 10.7546/nntdm.2020.26.4.63-67
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Authors and affiliations

Antoine Mhanna
SRS College Kleiat Lebanon


In this note we explain the two pseudo-Frobenius numbers for \langle m^2-n^2,m^2+n^2,2mn\rangle where m and n are two coprime numbers of different parity. This lets us give an Apéry set for these numerical semigroups.


  • Numerical semigroups
  • Primitive Pythagorean triplets
  • Pseudo-Frobenius number

2010 Mathematics Subject Classification

  • 11D07
  • 11D45
  • 11D85
  • 20M14


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Cite this paper

Mhanna, A. (2020). On Pythagorean triplet semigroups. Notes on Number Theory and Discrete Mathematics, 26 (4), 63-67, doi: 10.7546/nntdm.2020.26.4.63-67.

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