gcd-Pairs in ℤ_n and their graph representations

2022/06/03 by Tapanyo, Wanchai, Tongpikul, Tanyaton, Kaewpradit, Suphansa
#05C15 (Secondary) #05C38 #05C45 #11A05 (Primary) #11A41 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #G.2.2

paper · doi:10.48550/arxiv.2206.01847

Abstract

This research introduces a gcd-pair in ℤ_n which is an unordered pair \[a]_n, [b]_n\ of elements in ℤ_n such that 0≤ a,b < n and the greatest common divisor gcd(a,b) divides n . The properties of gcd-pairs in ℤ_n and their graph representations are investigated. We also provide the counting formula of gcd-pairs in ℤ_n and its subsets. The algorithms to find, count and check gcd-pairs in ℤ_n are included.

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