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 \(2x^2-1.\)
by
Calvin Lin