Equalities between greatest common divisors involving three coprime pairs

Rogelio Tomás García
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 3, Pages 5—7
DOI: 10.7546/nntdm.2020.26.3.5-7
Download full paper: PDF, 140 Kb

Details

Authors and affiliations

Rogelio Tomás García
CERN
Geneva, Switzerland

Abstract

A new equality of the greatest common divisor (gcd) of quantities involving three coprime pairs is proven in this note. For ai and bi positive integers such that gcd(ai, bi) = 1 for i ∈ {1, 2, 3} and dij = |aibj − ajbi|, then gcd(d32; d31) = gcd(d32; d21) = gcd(d31; d21): The proof uses properties of Farey sequences.

Keywords

  • Greatest common divisor
  • Farey
  • Equality

2010 Mathematics Subject Classification

  • 11A05
  • 11B57.

References

  1. Hardy, G. H., & Wright, E. M. (1996). An Introduction to the Theory of Numbers, Fifth Edition, Oxford Science Publications.

Related papers

Cite this paper

Tomás García, R. (2020). Equalities between greatest common divisors involving three coprime pairs. Notes on Number Theory and Discrete Mathematics, 26 (3), 5-7, doi: 10.7546/nntdm.2020.26.3.5-7.

Comments are closed.