A GENERALIZATION OF WOLSTENHOLME’S HARMONIC SERIES CONGRUENCE (2006)
by
Hao Pan
| Citations: | 4 - 0 self |
BibTeX
@MISC{Pan06ageneralization,
author = {Hao Pan},
title = {A GENERALIZATION OF WOLSTENHOLME’S HARMONIC SERIES CONGRUENCE},
year = {2006}
}
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Abstract
Abstract. Let A, B be two non-zero integers. Define the Lucas sequences {un} ∞ n=0 and {vn} ∞ n=0 by and u0 = 0, u1 = 1, un = Aun−1 − Bun−2 for n ≥ 2 v0 = 2, v1 = A, vn = Avn−1 − Bvn−2 for n ≥ 2. For any n ∈ Z +, let wn be the largest divisor of un prime to u1, u2,..., un−1. We prove that for any n ≥ 5 where ∆ = A 2 − 4B. n−1 vj uj j=1
