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SUPERCONGRUENCES INVOLVING
$p$-ADIC GAMMA FUNCTIONS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 98 / Issue 1 / August 2018
- Published online by Cambridge University Press:
- 30 May 2018, pp. 27-37
- Print publication:
- August 2018
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- Article
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We establish some supercongruences for the truncated
$_{2}F_{1}$ and 
$_{3}F_{2}$ hypergeometric series involving the 
$p$-adic gamma functions. Some of these results extend the four Rodriguez-Villegas supercongruences on the truncated 
$_{3}F_{2}$ hypergeometric series. Related supercongruences modulo 
$p^{3}$ are proposed as conjectures.
