Geodesic
Congruences involving alternating multiple harmonic sums
The electronic journal of combinatorics, Tome 17 (2010)
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We show that for any prime $p\neq 2$, $$\sum_{k=1}^{p-1}{(-1)^k\over k}{-{1\over 2} \choose k} \equiv -\sum_{k=1}^{(p-1)/2}{1\over k} \pmod{p^3}$$ by expressing the left-hand side as a combination of alternating multiple harmonic sums.
DOI : 10.37236/288
Classification : 11A07, 11B65, 05A19
Mots-clés : multiple harmonic sum, congruence, binomial coefficients, Bernoulli numbers, Fermat quotient 
@article{10_37236_288,
     author = {Roberto Tauraso},
     title = {Congruences involving alternating multiple harmonic sums},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/288},
     zbl = {1222.11006},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/288/}
}
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%J The electronic journal of combinatorics
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Roberto Tauraso. Congruences involving alternating multiple harmonic sums. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/288

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