RMO Practice Problem - Algebra 2

Algebra Level 5

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

ax17+bx16+1\large ax^{17} + bx^{16} +1

is divisible by x2x1x^2 - x -1.

Then find the sum of all such pairs.

Details and Assumptions:

  • If you get (2,3)(2,3) and (3,4)(3,4) as your answer, then express your answer as sum of all those values i.e. 2+3+3+4=122+3+3+4=12.

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