# Thread: Problem Of The Week #401 Jan 15th, 2020

1. Here is this week's POTW:

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Let $a>0$ and $P(x)$ be a polynomial with integer coefficients such that

$P(1)=P(3)=P(5)=P(7)=a$ and

$P(2)=P(4)=P(6)=P(8)=-a$.

What is the smallest possible value of $a$?

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2.

Congratulations to Opalg for his partial correct solution!

You can find the suggested solution as shown below: