Let a > 0, and let 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?

calicokittycat Sep 12, 2021

#2**+1 **

I have no idea how to do this. So if a mathematician wants to explain it that would be really good.

Of course, if the coefficients did not have to be integers then a could be as close to 0 as you please.

I did construct a graph of degree 7 but it is not actually helpful

Here is a link:

Melody Sep 14, 2021