{
  "id": "1708.08085",
  "version": "v1",
  "published": "2017-08-27T13:37:32.000Z",
  "updated": "2017-08-27T13:37:32.000Z",
  "title": "Valuations, arithmetic progressions, and prime numbers",
  "authors": [
    "Shin-ichiro Seki"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this short note, we give two proofs of the infinitude of primes via valuation theory and give a new proof of the divergence of the sum of prime reciprocals by Roth's theorem and Euler-Legendre's theorem for arithmetic progressions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-27T13:37:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A41",
      "11B25"
    ],
    "keywords": [
      "arithmetic progressions",
      "prime numbers",
      "short note",
      "roths theorem",
      "prime reciprocals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}