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Some curious congruences modulo primes

Number Theory 2010-02-25 v3 Combinatorics

Abstract

Let n be a positive odd integer and let p>n+1 be a prime. We mainly derive the following congruence: 0<i1<...<in<p(i1/3)(1)i1/(i1...in)=0(modp).\sum_{0<i_1<...<i_n<p}(i_1/3)(-1)^{i_1}/(i_1...i_n)=0 (mod p).

Keywords

Cite

@article{arxiv.0904.1162,
  title  = {Some curious congruences modulo primes},
  author = {Li-Lu Zhao and Zhi-Wei Sun},
  journal= {arXiv preprint arXiv:0904.1162},
  year   = {2010}
}

Comments

6 pages

R2 v1 2026-06-21T12:49:06.806Z