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P(x)P(x)P(x) is a cubic polynomial, and for x=1, 2, 3, 4,x=1,~2,~3,~4,x=1, 2, 3, 4, P(x)=11+x+x2.P(x)=\frac{1}{1+x+x^2}.P(x)=1+x+x21.
For some positive coprime integers aaa and b,b,b, P(5)=−ab.P(5)=-\frac{a}{b}.P(5)=−ba.
Find the value of a+b.a+b.a+b.
This problem is a part of <Christmas Streak 2017> series.
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