{
  "id": "1312.3531",
  "version": "v1",
  "published": "2013-12-12T15:59:57.000Z",
  "updated": "2013-12-12T15:59:57.000Z",
  "title": "On equal values of power sums of arithmetic progressions",
  "authors": [
    "A. Bazsó",
    "D. Kreso",
    "F. Luca",
    "Á. Pintér"
  ],
  "comment": "This version differs slightly from the published version in its exposition",
  "journal": "Glas. Mat., 47, 2012, 253--263",
  "doi": "10.3336/gm.47.2.02",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we consider the Diophantine equation \\begin{align*}b^k +\\left(a+b\\right)^k &+ \\cdots + \\left(a\\left(x-1\\right) + b\\right)^k=\\\\ &=d^l + \\left(c+d\\right)^l + \\cdots + \\left(c\\left(y-1\\right) + d\\right)^l, \\end{align*} where $a,b,c,d,k,l$ are given integers. We prove that, under some reasonable assumptions, this equation has only finitely many integer solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-12T15:59:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B68",
      "11D41"
    ],
    "keywords": [
      "arithmetic progressions",
      "power sums",
      "equal values",
      "diophantine equation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.3531B"
    }
  }
}