{
  "id": "1109.2340",
  "version": "v3",
  "published": "2011-09-11T19:10:10.000Z",
  "updated": "2011-10-19T17:56:41.000Z",
  "title": "An Extension of a Congruence by Kohnen",
  "authors": [
    "Romeo Mestrovic"
  ],
  "comment": "13 pages; This is the same as version 2 with extended Remarks on page 3 concerning a search of Euler numbers arising supercongruences and a new conjecture on page 4",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p>3$ be a prime, and let $q_p(2)=(2^{p-1}-1)/p$ be the Fermat quotient of $p$ to base 2. Recently, Z. H. Sun proved that \\sum_{k=1}^{p-1}\\frac{1}{k\\cdot 2^k}\\equiv q_p(2)-\\frac{p}{2}q_p(2)^2 \\pmod{p^2} which is a generalization of a congruence due to W. Kohnen. In this note we give an elementary proof of the above congruence which is based on several combinatorial identities and congruences involving the Fermat quotient $q_p(2)$, harmonic or alternating harmonic sums.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-10-19T17:56:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B75",
      "11A07",
      "11B65",
      "05A10"
    ],
    "keywords": [
      "congruence",
      "fermat quotient",
      "elementary proof",
      "combinatorial identities",
      "alternating harmonic sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.2340M"
    }
  }
}