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arXiv · 0904.1162

Some curious congruences modulo primes

Li-Lu Zhao·Zhi-Wei Sun
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Abstract

Let n be a positive odd integer and let p>n+1 be a prime. We mainly derive the following congruence: $$\sum_{0<i_1<...<i_n<p}(i_1/3)(-1)^{i_1}/(i_1...i_n)=0 (mod p).$$

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Li-Lu Zhao, Zhi-Wei Sun. 2010-02-25. Some curious congruences modulo primes. https://arxiv.org/abs/0904.1162

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