Result: A simple proof of a curious congruence by Zhao

Title:
A simple proof of a curious congruence by Zhao
Authors:
Chun-Gang Ji
Source:
Proceedings of the American Mathematical Society. 133:3469-3472
Publisher Information:
American Mathematical Society (AMS), 2005.
Publication Year:
2005
Subject Terms:
0301 basic medicine, 03 medical and health sciences, congruences involving Bernoulli numbers, Kummer congruence, Congruences, primitive roots, residue systems, Wolstenholme's theorem, 0101 mathematics, Bernoulli and Euler numbers and polynomials, 01 natural sciences, Primes, prime number
Document Type:
Academic journal Article<br />Other literature type
File Description:
application/xml
Language:
English
ISSN:
1088-6826
0002-9939
DOI:
10.1090/s0002-9939-05-07939-6
Access URL:
https://www.ams.org/proc/2005-133-12/S0002-9939-05-07939-6/S0002-9939-05-07939-6.pdf
https://zbmath.org/2199859
https://doi.org/10.1090/s0002-9939-05-07939-6
https://www.ams.org/journals/proc/2005-133-12/S0002-9939-05-07939-6/home.html
https://dialnet.unirioja.es/servlet/articulo?codigo=1377304
https://www.jstor.org/stable/4097488
Rights:
URL: https://www.ams.org/publications/copyright-and-permissions
Accession Number:
edsair.doi.dedup.....015ccd7fcbfb5aad28f5976edd78db00
Database:
OpenAIRE

Further Information

The author gives a simple proof of the following curious congruence for odd prime p > 3 p>3 which was established by Jianqiang Zhao: ∑ i + j + k = p i , j , k > 0 1 i j k ≡ − 2 B p − 3 ( mod p ) . \begin{equation*}\sum _{\substack {{i+j+k=p} {i,\ j,\ k>0}}}\frac {1}{ijk}\equiv -2B_{p-3}(\text {mod}\ p).\end{equation*}