RMO Practice Problem - Algebra 2

Algebra Level 5

Let \((a,b)\) be the pair of integers such that

\[\large ax^{17} + bx^{16} +1\]

is divisible by \(x^2 - x -1\).

Then find the sum of all such pairs.

Details and Assumptions:

If you get \((2,3)\) and \((3,4)\) as your answer, then express your answer as sum of all those values i.e. \(2+3+3+4=12\).

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