# 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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