Mathematics – Number Theory
Scientific paper
2009-05-20
Mathematics
Number Theory
Scientific paper
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.
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