Document Type
Conference Proceeding
Publication Date
5-31-2022
Abstract
We consider the second order linear recurrence Un+2 = P Un+1 − QUn, with P and Q in Z and initial conditions U0 = 0 and U1 = 1. We show that for all integers r, s, k, l such that r + s = k + l, and Gn, Hn satisfying the recurrence relation and initial conditions G0, G1 and H0, H1 respectively, we have GrHs − GkHl = Qt (Gr−tHs−t − Gk−tHl−t) for all integers t. We also give a relationship between the period and the rank of appearance when the recurrence is considered over Zp. We obtain as a corollary that the period of the Fibonacci sequence is always even.
Recommended Citation
Reyes, Jesús Jiménez, "Identities, Rank of Appearance, and Period of Second Order Linear Recurrences" (2022). ACMS Conference Proceedings 2022. 21.
https://pillars.taylor.edu/acms-2022/21