Christmas Streak 32/88: Polynomial But Strange

Algebra Level 3

P(x)P(x) is a cubic polynomial, and for x=1, 2, 3, 4,x=1,~2,~3,~4, P(x)=11+x+x2.P(x)=\frac{1}{1+x+x^2}.

For some positive coprime integers aa and b,b, P(5)=ab.P(5)=-\frac{a}{b}.

Find the value of a+b.a+b.


This problem is a part of <Christmas Streak 2017> series.

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