Some curious congruences modulo primes
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congruencecongruencescuriousderivefollowingintegermainlymodulo
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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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