MathDB

Putnam 2016 A1

Source:

December 4, 2016

PutnamPutnam 2016Putnam easyPutnam number theory

Problem Statement

Find the smallest positive integer

j

such that for every polynomial

p(x)

with integer coefficients and for every integer

k,

the integer

p^{(j)}(k)=\left. \frac{d^j}{dx^j}p(x) \right|_{x=k}

(the

j

-th derivative of

p(x)

at

k

) is divisible by

2016.

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