A GCD problem and a Hessenberg determinant

M. Hariprasad
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 2, Pages 28—31
DOI: 10.7546/nntdm.2018.24.2.28-31
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Authors and affiliations

M. Hariprasad
Department of Computational and Data Sciences
Indian Institute of Science, Bangalore-560012, India

Abstract

In this article we give a proof that, when two integers a and b are coprime ((a, b) = 1, i.e., greatest common divisor (GCD) of a and b is 1), then GCD of a + b and (ap + bp)/(a + b) is either 1 or p for a prime number p. We prove this by linking the problem to a certain type of Hessenberg determinants.

Keywords

  • Greatest common divisor
  • Binomial coefficients
  • Hessenberg determinants

2010 Mathematics Subject Classification

  • 11A05
  • 15B36
  • 11C20

References

  1. Apostol, T. M. (2013) Introduction to Analytic Number Theory, Springer Science & Business Media.

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Cite this paper

APA

Hariprasad, M. (2018). A GCD problem and a Hessenberg determinant. Notes on Number Theory and Discrete Mathematics, 24(2), 28-31, doi: 10.7546/nntdm.2018.24.2.28-31.

Chicago

Hariprasad, M. “A GCD Problem and a Hessenberg Determinant.” Notes on Number Theory and Discrete Mathematics 24, no. 2 (2018): 28-31, doi: 10.7546/nntdm.2018.24.2.28-31.

MLA

Hariprasad, M. “A GCD Problem and a Hessenberg Determinant.” Notes on Number Theory and Discrete Mathematics 24.2 (2018): 28-31. Print, doi: 10.7546/nntdm.2018.24.2.28-31.

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