MathDB
Korea Second Round 2011

Source: Korea Second Round 2011 #5

August 21, 2011
number theory unsolvednumber theory

Problem Statement

Find the number of positive integer n<38 n < 3^8 satisfying the following condition.
"The number of positive integer k(1≤k≤n3)k (1 \leq k \leq \frac {n}{3}) such that n!(n−3k)!⋅k!⋅3k+1 \frac{n!}{(n-3k)! \cdot k! \cdot 3^{k+1}} is not a integer" is 216 216 .
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