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Supercongruences for a truncated hypergeometric series

Published 22 Jul 2010 in math.NT and math.CO | (1007.3852v2)

Abstract: The purpose of this note is to obtain some congruences modulo a power of a prime $p$ involving the truncated hypergeometric series $$\sum_{k=1}{p-1} {(x)_k(1-x)_k\over (1)_k2}\cdot{1\over ka}$$ for $a=1$ and $a=2$. In the last section, the special case $x=1/2$ is considered.

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