Amelioration of Glaisher's Congruence

Abstract : We prove that if $p\geq 5$ is a prime, then \begin{equation*} \frac{2^{p-1}-1}{p}\equiv -\frac{1}{2}\left( \sum_{k=1}^{p-1}\frac{2^{k}}{k}% \right)(\bmod p^{2}) \end{equation*}
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Submitted on : Monday, July 4, 2016 - 11:54:04 AM
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Scheherazade Zerroukhat, Redha Chellal, Farid Bencherif. Amelioration of Glaisher's Congruence. 2016. 〈hal-01341168〉

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