MathDB
2015-2016 Fall OMO #28

Source:

November 18, 2015
Online Math Open

Problem Statement

Let NN be the number of 20152015-tuples of (not necessarily distinct) subsets (S1,S2,…,S2015)(S_1, S_2, \dots, S_{2015}) of {1,2,…,2015}\{1, 2, \dots, 2015 \} such that the number of permutations σ\sigma of {1,2,…,2015}\{1, 2, \dots, 2015 \} satisfying σ(i)∈Si\sigma(i) \in S_i for all 1≤i≤20151 \le i \le 2015 is odd. Let k2,k3k_2, k_3 be the largest integers such that 2k2∣N2^{k_2} | N and 3k3∣N3^{k_3} | N respectively. Find k2+k3.k_2 + k_3.
Proposed by Yang Liu
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