Journal of Integer Sequences, Vol. 28 (2025), Article 25.2.2

Greatest Common Divisors and Lucas's Theorem


John Ferdinands
Department of Mathematics and Statistics
Calvin University
3201 Burton St. SE
Grand Rapids, MI 49546
USA

Timothy Ferdinands
Department of Mathematics and Computer Science
Alfred University
One Saxon Dr.
Alfred, NY 14802
USA

Abstract:

We consider a sequence of greatest common divisors of the coefficients of a binomial expansion and use a classical result due to Lucas to show that the greatest common divisor is always 1. Our result generalizes a problem found in the Problem Section of Mathematics Magazine.

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(Concerned with sequences A007318.)

Received June 11 2024; revised versions received June 20 2024; June 21 2024; January 15 2025; March 4 2025. Published in Journal of Integer Sequences, March 10 2025.

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