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0<k< n^2/4, k has no prime divisor > n, then k divides n!

Source: Austrian Polish 1986 APMC

April 30, 2020
factorialdividesprime divisors

Problem Statement

Let kk and nn be integers with 0<k<n2/40 < k < n^2/4 such that k has no prime divisor greater than nn. Prove that kk divides n!n!.
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