MathDB

4

Part of 2014 Dutch BxMO/EGMO TST

Problems(1)

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

Source: Dutch BxMO/EGMO Team Selection Test 2014 P4

7/17/2014
Let m≥3m\ge 3 and nn be positive integers such that n>m(m−2)n>m(m-2). Find the largest positive integer dd such that d∣n!d\mid n! and k∤dk\nmid d for all k∈{m,m+1,…,n}k\in\{m,m+1,\ldots,n\}.
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