Document Type

Conference Proceeding

Publication Date



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.