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Congruences for finite triple harmonic sums

✍ Scribed by Xu-dan Fu; Xia Zhou; Tian-xin Cai


Book ID
111840713
Publisher
SP Zhejiang University Press
Year
2007
Tongue
English
Weight
188 KB
Volume
8
Category
Article
ISSN
1009-3095

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πŸ“œ SIMILAR VOLUMES


Sums of Triple Harmonic Series
✍ Michael E. Hoffman; Courtney Moen πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 162 KB

For positive integers a, b, c with a 2, let A(a, b, c) denote the triple harmonic series We show that the sum of the A(a, b, c) with a+b+c=n is `(n)= i 1 1Γ‚i n . A similar identity for double harmonic series goes back to Euler.

Congruences for Jacobi Sums
✍ Ronald Evans πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 249 KB

A congruence for Jacobi sums of order k over finite fields is proved, which generalizes a congruence of for prime k and Ihara (1986) for prime power k. Related congruences for Jacobi sums are also presented. The techniques are elementary and self-contained, in contrast with the deep methods of Iwas

Congruences for sums of binomial coeffic
✍ Zhi-Wei Sun; Roberto Tauraso πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 135 KB

Let q > 1 and m > 0 be relatively prime integers. We find an explicit period Ξ½ m (q) such that for any integers n > 0 and r we have whenever a is an integer with gcd(1 -(-a) m , q) = 1, or a ≑ -1 (mod q), or a ≑ 1 (mod q) and 2 | m, where n r m (a) = k≑r (mod m) n k a k . This is a further extensio

Bounds for Certain Harmonic Sums
✍ B.J. English; G. Rousseau πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 161 KB

The monotonicity properties of the function y1 y1 y1 ⌽ n s pn q r q 1 q pn q r q 2 q иии q qn q s Ž . Ž . Ž . Ž . are determined, where p, q, r, and s are fixed integers such that 0pq and 0 F p q rq q s. The results extend earlier results of Adamovic and Taskovic ´Ž . Ž . 1969 and Simic 1979 for t