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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## Details

### 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 (*a ^{p}* +

*b*)/(

^{p}*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

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

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## Cite this paper

APAHariprasad, 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.

ChicagoHariprasad, 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.

MLAHariprasad, 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.