Arithmetic-Term Representations for the Greatest Common Divisor

2024/11/10 by Mihai Prunescu, Prunescu, Mihai, Joseph Shunia +1 · 3 citations
Mathematics · #05A15 #11A05 #11B37 #Algebraic Geometry and Number Theory #Algebraic and Geometric Analysis #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2411.06430

openalex publication_date 2024/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We construct a new arithmetic-term representation for the function gcd(a,b). As a byproduct, we also deduce a representation gcd(a,b) by a modular term in integer arithmetic.

Cited by

• Arithmetic closed forms count the Mersenne primes, the Fermat primes and the twin-prime pairs
• Elementary closed-forms for non-trivial divisors
• A Minimal Substitution Basis for the Kalmar Elementary Functions

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