Computing the Greatest Common Divisor of Binomial Coefficients C(mn, mk)

Authors

• Chai Wah Wu, International Business MachinesFollow

DOI Link

https://doi.org/10.70013/c792j2mn

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 + p^j. 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.

Author ORCID Identifier

0000-0002-0657-0683

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

Wu, Chai Wah (2026) "Computing the Greatest Common Divisor of Binomial Coefficients C(mn, mk)," Communications on Number Theory and Combinatorial Theory: Vol. 7, Article 4.
DOI: 10.70013/c792j2mn
Available at: https://research.library.kutztown.edu/contact/vol7/iss1/4