## Congruences involving alternating multiple harmonic sum

Tauraso, Roberto
##### Description
We show that for any prime prime $p\not=2$ $$\sum_{k=1}^{p-1} {(-1)^k\over k}{-{1\over 2} \choose k} \equiv -\sum_{k=1}^{(p-1)/2}{1\over k} \pmod{p^3}$$ by expressing the l.h.s. as a combination of alternating multiple harmonic sums.
##### Keywords
Mathematics - Number Theory, 11A07, 11B65 (Primary) 05A10, 05A19 (Secondary)