{
  "id": "2109.13174",
  "version": "v2",
  "published": "2021-09-27T16:33:37.000Z",
  "updated": "2022-03-07T15:35:49.000Z",
  "title": "Representation of even integers as a sum of squares of primes and powers of two",
  "authors": [
    "Shehzad Hathi"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In 1951, Linnik proved the existence of a constant $K$ such that every sufficiently large even number is the sum of two primes and at most $K$ powers of 2. Since then, this style of approximation has been considered for problems similar to the Goldbach conjecture. One such problem is the representation of a sufficiently large even number as a sum of four squares of primes and at most $k$ powers of two. In 2014, Zhao proved $k = 46$. In this paper, we improve upon this result by proving $k = 31$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-03-07T15:35:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P55",
      "11P32"
    ],
    "keywords": [
      "representation",
      "sufficiently large",
      "goldbach conjecture",
      "problems similar",
      "approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}