{
  "id": "1901.07882",
  "version": "v1",
  "published": "2019-01-20T11:56:49.000Z",
  "updated": "2019-01-20T11:56:49.000Z",
  "title": "Goldbach's like conjectures arising from arithmetic progressions whose first two terms are primes",
  "authors": [
    "Romeo Meštrović"
  ],
  "comment": "5 pages, no figures, no tables",
  "categories": [
    "math.NT"
  ],
  "abstract": "For two odd primes $p$ and $q$ such that $p<q$, let $A(p,q):=(a_k)_{k=1}^{\\infty}$ be the arithmetic progression whose $k$th term is given by $a_k=(k-1)(q-p)+p$ (i.e., with $a_1=p$ and $a_2=q$). Here we conjecture that for every positive integer $a>1$ there exist a positive integer $n$ and two odd primes $p$ and $q$ such that $a$ can be expressed as a sum of the first $2n$ terms of the arithmetic progression $A(p,q)$. Notice that in the case of even $a$, this conjecture immediately follows from Goldbach's conjecture. We also propose the analogous conjecture for odd positive integers $a>1$ as well as some related Goldbach's like conjectures arising from the previously mentioned arithmetic progressions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-20T11:56:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A41",
      "11A07",
      "11A25"
    ],
    "keywords": [
      "conjectures arising",
      "odd primes",
      "goldbachs conjecture",
      "th term",
      "mentioned arithmetic progressions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}