Year: 2026
Type: article
Abstract: The greatest common divisor (GCD) of C(2n,2k) for 1 ≤ k < n is known to be some power of 2 times the product of all odd primes p such that 2n = pi + pj. We complete the analysis of this GCD by showing that its 2-adic valuation is at most 1 and relates it to Mersenne primes. We also show how to efficiently compute GCD {C(mn,mk) : 1 ≤ k < n} when n and m satisfy certain conditions.
DOI: 10.70013/c792j2mn
Author: Chai Wah Wu
Institution: IBM (United States)
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7222928453