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A Simple Proof of a Curious Congruence by Sun

Proceedings of the American Mathematical Society / v.127 no.5. 1999, pp.1289-1291

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Abstract : In this note, we give a simple and elementary proof of the following curious congruence which was established by Zhi-Wei Sun: $\sum_{k=1}^{(p-1)/2}\frac{1}{k\cdot 2^{k}}\equiv \sum_{k=1}^{[3p/4]}\frac{(-1)^{k-1}}{k}\quad (\text{mod}\,p)$ .

Keyword : Primary 11A07, 11A41

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