1967 IMO Problems/Problem 3

Revision as of 14:32, 17 February 2018 by Durianaops (talk | contribs) (Created page with "Let <math>k, m, n</math> be natural numbers such that <math>m+k+1</math> is a prime greater than <math>n+1.</math> Let <math>c_s=s(s+1).</math> Prove that the product <cmath>(...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Let $k, m, n$ be natural numbers such that $m+k+1$ is a prime greater than $n+1.$ Let $c_s=s(s+1).$ Prove that the product \[(c_{m+1}-c_k)(c_{m+2}-c_k)\cdots (c_{m+n}-c_k)\] is divisible by the product $c_1c_2\cdots c_n$.