Congruences for finite triple harmonic sums
β 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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π SIMILAR VOLUMES
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 1Γi n . A similar identity for double harmonic series goes back to Euler.
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
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 β‘ -1 (mod q), or a β‘ 1 (mod q) and 2 | m, where n r m (a) = kβ‘r (mod m) n k a k . This is a further extensio
The monotonicity properties of the function y1 y1 y1 β½ n s pn q r q 1 q pn q r q 2 q ΠΈΠΈΠΈ q qn q s Ε½ . Ε½ . Ε½ . Ε½ . 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 Β΄Ε½ . Ε½ . 1969 and Simic 1979 for t