Mattarei, Sandro
(2006)
On a special congruence of Carlitz.
Integers, 6
.
A9, 13 pp. (electronic).
ISSN 1553-1732
Full content URL: https://arxiv.org/abs/math/0602012
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| Item Type: | Article |
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| Item Status: | Live Archive |
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Abstract
We prove that if q is a power of a prime p and p
k
divides
a, with k ≥ 0, then
1 + (q − 1) X
0≤b(q−1)<a
a
b(q − 1)!
≡ 0 (mod p
k+1).
The special case of this congruence where q = p was proved by Carlitz
in 1953 by means of rather deep properties of the Bernoulli numbers.
A more direct approach produces our generalization and several related
results.
| Additional Information: | The preprint version of this article can be accessed freely online at https://arxiv.org/abs/math/0602012 |
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| Keywords: | Binomial coefficient sum |
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| Related URLs: | |
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| ID Code: | 18534 |
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| Deposited On: | 25 Jul 2018 10:28 |
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