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SMT 2023 Algebra #7

Source:

May 3, 2023

Problem Statement

Consider a sequence F0=2F_0=2, F1=3F_1=3 that has the property Fn+1Fn−1−Fn2=(−1)n⋅2F_{n+1}F_{n-1}-F_n^2=(-1)^n\cdot2. If each term of the sequence can be written in the form a⋅r1n+b⋅r2na\cdot r_1^n+b\cdot r_2^n, what is the positive difference between r1r_1 and r2r_2?
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