# 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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