Congruences involving alternating multiple harmonic sum

Abstract

We show that for any prime prime $p\ne 2$ $$\sum _{k=1}^{p-1}\frac{(-1{)}^k}{k}\left(\genfrac{}{}{0ex}{}{-\frac{1}{2}}{k}\right)\equiv -\sum _{k=1}^{(p-1)/2}\frac{1}{k}(\mathrm{mod}{p}^3)$$ by expressing the l.h.s. as a combination of alternating multiple harmonic sums.

References in corpus (1)

• Some curious congruences modulo primes

Cited by in corpus (2)

• Congruences of alternating multiple harmonic sums
• Two supercongruences related to multiple harmonic sums