1IMATE, UNAM Ap. Postal 61-3 (Xangari), CP. 58 089 Morelia, Michoacán, Mexico 2Department of Mathematics Auburn University Montgomery Montgomery, AL 36124-4023, U.S.A.
Colloquium Mathematicum, Tome 96 (2003) no. 2, pp. 191-205
We show that if $p\ne 5$
is a prime, then the numbers
$$
\left\{{1 \over p}
\left({p\atop {m_1,\dots,m_t}}\right)
\biggm| t\ge 1,\, m_i\ge 0\ \hbox{for}\ i=1,\dots,t
\ \hbox{and}~\sum_{i=1}^t m_i=p\right\}
$$
cover all the nonzero residue
classes modulo $p$.
Keywords:
prime numbers atop dots right biggm hbox dots hbox sum p right cover nonzero residue classes modulo
Affiliations des auteurs :
Florian Luca
1
;
Pantelimon Stănică
2
1
IMATE, UNAM Ap. Postal 61-3 (Xangari), CP. 58 089 Morelia, Michoacán, Mexico
2
Department of Mathematics Auburn University Montgomery Montgomery, AL 36124-4023, U.S.A.
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author = {Florian Luca and Pantelimon St\u{a}nic\u{a}},
title = {Products of factorials modulo $p$},
journal = {Colloquium Mathematicum},
pages = {191--205},
year = {2003},
volume = {96},
number = {2},
doi = {10.4064/cm96-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm96-2-4/}
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TY - JOUR
AU - Florian Luca
AU - Pantelimon Stănică
TI - Products of factorials modulo $p$
JO - Colloquium Mathematicum
PY - 2003
SP - 191
EP - 205
VL - 96
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4064/cm96-2-4/
DO - 10.4064/cm96-2-4
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