MathDB
2015-2016 Spring OMO #28

Source:

March 29, 2016
Online Math Open

Problem Statement

Let NN be the number of polynomials P(x1,x2,…,x2016)P(x_1, x_2, \dots, x_{2016}) of degree at most 20152015 with coefficients in the set {0,1,2}\{0, 1, 2 \} such that P(a1,a2,⋯ ,a2016)≡1(mod3)P(a_1,a_2,\cdots ,a_{2016}) \equiv 1 \pmod{3} for all (a1,a2,⋯ ,a2016)∈{0,1}2016.(a_1,a_2,\cdots ,a_{2016}) \in \{0, 1\}^{2016}.
Compute the remainder when v3(N)v_3(N) is divided by 20112011, where v3(N)v_3(N) denotes the largest integer kk such that 3k∣N.3^k | N.
Proposed by Yang Liu
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