MathDB
2017-2018 Spring OMO Problem 19

Source:

April 3, 2018

Problem Statement

Let P(x)P(x) be a polynomial of degree at most 20182018 such that P(i)=(2018i)P(i)=\binom{2018}i for all integer ii such that 0≤i≤20180\le i\le 2018. Find the largest nonnegative integer nn such that 2n∣P(2020)2^n\mid P(2020).
Proposed by Michael Ren
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