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    Supercongruences for a truncated hypergeometric series

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    The purpose of this note is to obtain some congruences modulo a power of a prime pp involving the truncated hypergeometric series βˆ‘k=1pβˆ’1(x)k(1βˆ’x)k(1)k2β‹…1ka\sum_{k=1}^{p-1} {(x)_k(1-x)_k\over (1)_k^2}\cdot{1\over k^a} for a=1a=1 and a=2a=2. In the last section, the special case x=1/2x=1/2 is considered.Comment: Revised versio
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