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Divisor of n! that does not have factors from m to n.

Source: Dutch BxMO/EGMO Team Selection Test 2014 P4

July 17, 2014

number theory proposednumber theory

Problem Statement

Let

m\ge 3

and

n

be positive integers such that

n>m(m-2)

. Find the largest positive integer

d

such that

d\mid n!

and

k\nmid d

for all

k\in\{m,m+1,\ldots,n\}