MathDB

7

Part of 1986 Austrian-Polish Competition

Problems(1)

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

Source: Austrian Polish 1986 APMC

4/30/2020
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!.
factorialdividesprime divisors