{
  "id": "1708.06951",
  "version": "v1",
  "published": "2017-08-23T10:58:55.000Z",
  "updated": "2017-08-23T10:58:55.000Z",
  "title": "Squares in arithmetic progressions and infinitely many primes",
  "authors": [
    "Andrew Granville"
  ],
  "comment": "To appear in the American Mathematical Monthly",
  "categories": [
    "math.NT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-23T10:58:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11A41",
      "11B25"
    ],
    "keywords": [
      "arithmetic progression",
      "van der waerdens theorem",
      "fermats theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}