23
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      The Nagell-Ljunggren equation via Runge's method

      Preprint
      ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          The Diophantine equation (x^n-1)/(x-1)=y^q has four known solutions in integers x, y, q and n with |x|, |y|, q > 1 and n > 2. Whilst we expect that there are, in fact, no more solutions, such a result is well beyond current technology. In this paper, we prove that if (x,y,n,q) is a solution to this equation, then n has three or fewer prime divisors, counted with multiplicity. This improves a result of Bugeaud and Mihailescu.

          Related collections

          Most cited references5

          • Record: found
          • Abstract: not found
          • Article: not found

          Subgroups of prime power index in a simple group

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            New bounds and conditions for the equation of Nagell–Ljunggren

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              On the Diophantine equation (xn- 1)/(x-1) = yq

                Bookmark

                Author and article information

                Journal
                14 December 2013
                Article
                1312.4037
                f1d8c9fa-20c6-4287-a7b0-e291dc3f7a5d

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                11D61
                math.NT

                Comments

                Comment on this article