Tri-ratio

Algebra Level 5

Find the sum of all positive integers \(a\) such that for some positive integer \(b\) the ratio \[\frac{x^b+x-1}{x^a+x^2-1}\] is a polynomial in \(x.\)

Details and assumptions

If \(a=2,\) then the denominator is \(2x^2-1.\)

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