Tri-ratio

Algebra Level 5

Find the sum of all positive integers aa such that for some positive integer bb the ratio xb+x1xa+x21\frac{x^b+x-1}{x^a+x^2-1} is a polynomial in x.x.

Details and assumptions

If a=2,a=2, then the denominator is 2x21.2x^2-1.

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