An identity involving the least common multiple of binomial coefficients and its application

2009/06/12 by Bakir Farhi, Farhi, Bakir · 1 citation
Mathematics · #11A05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A05

paper · pdf · doi:10.48550/arxiv.0906.2295

5 pages. To appear in American Mathematical Monthly

arxiv created 2009/06/13 · arxiv updated 2009/12/01

Abstract

In this paper, we prove the identity \lcm\\binomk0, \binomk1, >..., \binomkk\ = (\lcm(1, 2, ..., k, k + 1))/(k + 1) (∀ k ∈ ℕ) . As an application, we give an easily proof of the well-known nontrivial lower bound \lcm(1, 2, ..., k) ≥ 2^{k - 1} (∀ k ≥ 1).

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