English

Squares in arithmetic progressions and infinitely many primes

Number Theory 2017-08-24 v1

Abstract

We give a new proof that there are infinitely many primes, relying on van der Waerden's theorem for coloring the integers, and Fermat's theorem that there cannot be four squares in an arithmetic progression. We go on to discuss where else these ideas have come together in the past.

Keywords

Cite

@article{arxiv.1708.06951,
  title  = {Squares in arithmetic progressions and infinitely many primes},
  author = {Andrew Granville},
  journal= {arXiv preprint arXiv:1708.06951},
  year   = {2017}
}

Comments

To appear in the American Mathematical Monthly

R2 v1 2026-06-22T21:21:35.801Z