ON THE MERCA'S CONNECTION BETWEEN THE PARTITION FUNCTION AND EULER'S TOTIENT

ON THE MERCA'S CONNECTION BETWEEN THE PARTITION FUNCTION AND EULER'S TOTIENT

Authors

  • Mateus Alegri Universidade Federal de Sergipe
  • José Luís Bonilla
  • J. Prajapati

DOI:

https://doi.org/10.34179/revisem.v9i3.21794

Abstract

We employ the Z-transform to study a result of Merca involving the partition function $p(n)$ and Euler's totient. Besides, we obtain an identity valid for pentagonal numbers and an arbitrary prime number.

Keywords: Partition function, Dirichlet character, Euler totient function, Z-transform, Möbius function.

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Published

2024-10-14

How to Cite

Alegri, M., Bonilla, J. L., & Prajapati, J. (2024). ON THE MERCA’S CONNECTION BETWEEN THE PARTITION FUNCTION AND EULER’S TOTIENT. Revista Sergipana De Matemática E Educação Matemática, 9(3), 136–143. https://doi.org/10.34179/revisem.v9i3.21794

Issue

Vol. 9 No. 3 (2024): Revista Sergipana de Matemática e Educação Matemática

Section

Mathematics

License

Copyright (c) 2024 Mateus Alegri

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