2 5 N ov 2 00 9 Preprint , arXiv : 0911 . 4433 ARITHMETIC THEORY OF HARMONIC NUMBERS
نویسندگان
چکیده
Harmonic numbers H k = P 0 3 be a prime. We show that p−1
منابع مشابه
O ct 2 01 1 Preprint , arXiv : 0911 . 4433 v 7 ARITHMETIC THEORY OF HARMONIC NUMBERS ( II )
For k = 0, 1, 2,. .. let H k denote the harmonic number 0 3 we have p−1 k=1
متن کاملN ov 2 00 9 Preprint , arXiv : 0910 . 5667 ON SUMS OF BINOMIAL COEFFICIENTS
Let p be an odd prime and a be a positive integer. In this paper we investigate the sum P p
متن کامل1 9 A ug 2 00 9 Preprint , arXiv : 0810 . 0467 LINEAR EXTENSION OF THE ERDŐS - HEILBRONN CONJECTURE
The famous Erd˝ os-Heilbronn conjecture plays an important role in the development of additive combinatorics. In 2007 Z. W. Sun made the following further conjecture (which is the linear extension of the Erd˝ os-Heilbronn conjecture): For any finite subset A of a field F and nonzero elements a where p(F) is the additive order of the multiplicative identity of F , and δ ∈ {0, 1} takes the value ...
متن کامل5 M ay 2 00 9 Preprint , arXiv : 0905 . 0635 ON UNIVERSAL SUMS OF POLYGONAL NUMBERS
For m = 3, 4, . . . , the polygonal numbers of order m are given by pm(n) = (m−2) ` n 2 ́ +n (n = 0, 1, 2, . . . ). For positive integers a, b, c and i, j, k > 3 with max{i, j, k} > 5, we call the triple (api, bpj , cpk) universal if for any n = 0, 1, 2, . . . there are nonnegative integers x, y, z such that n = api(x) + bpj(y) + cpk(z). We show that there are only 95 candidates for universal tr...
متن کاملJ ul 2 00 9 Preprint , arXiv : 0810 . 0467 LINEAR EXTENSION OF THE ERDŐS - HEILBRONN CONJECTURE
The famous Erd˝ os-Heilbronn conjecture plays an important role in the development of additive combinatorics. In 2007 Z. W. Sun made the following further conjecture (which is the linear extension of the Erd˝ os-Heilbronn conjecture): For any finite subset A of a field F and nonzero elements a where p(F) is the additive order of the multiplicative identity of F , and δ ∈ {0, 1} takes the value ...
متن کامل