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Find the least positive number m such that for any polynimial f(x) with real coefficients, there is a polynimial g(x) with real coefficients (degree not greater than m) such that there exist 2017 distinct number

a_1,a_2,...,a_{2017}

such that

g(a_i)=f(a_{i+1})

for i=1,2,...,2017 where indices taken modulo 2017.

Problem Statement