An alternative proof of Sylvester's theorem and variations for more primes

Steven Brown

An alternative proof of Sylvester's theorem and variations for more primes

Number Theory 2023-03-10 v1

Authors: Steven Brown

Abstract

This document presents an alternative proof of Sylvester's theorem stating that "the product of $n$ consecutive numbers strictly greater than $n$ is divisible by a prime strictly greater than $n$ ". In addition, the paper proposes stronger versions of Sylvester's theorem and Bertrand's postulate with more primes, as well as an approach to get more results in this direction.

Keywords

sylvester's theorem bertrand's postulate consecutive integers prime divisor alternative proof

Cite

@article{arxiv.2303.05395,
  title  = {An alternative proof of Sylvester's theorem and variations for more primes},
  author = {Steven Brown},
  journal= {arXiv preprint arXiv:2303.05395},
  year   = {2023}
}

Comments

8 pages

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