# 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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Remember to read the "POTW submission guidelines to find out how to "submit your answers!

2.

Congratulations to Opalg for his partial correct solution!

You can find the suggested solution as shown below:

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