Some Wolstenholme type congruences
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2013
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Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky
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Abstract
In this paper we give an extension and another proof of the following
Wolstenholme's type curious congruence established in 2008 by J. Zhao. Let s and
l be two positive integers and let p be a prime such that p ls + 3. Then
H(fsgl; p1) S(fsgl; p1)
8>><
>>:
s(ls + 1)p2
2(ls + 2)
Bpls2 (mod p3) if 2 - ls
(1)l1 sp
ls + 1
Bpls1 (mod p2) if 2 j ls:
APs an application, for given prime p 5, we obtain explicit formulae for the sum
1 k1< <kl p1 1=(k1 kl) (mod p3) if k 2 f1; 3; : : : ; p 2g, and for the sum P
1 k1< <kl p1 1=(k1 kl) (mod p2) if k 2 f2; 4; : : : ; p 3g
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Mathematics for Applications. 2013, 2, č. 1, s. 35-42. ISSN 1805-3629.
http://ma.fme.vutbr.cz/archiv/2_1/mestrovic_final.pdf
http://ma.fme.vutbr.cz/archiv/2_1/mestrovic_final.pdf
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en
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© Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky