• On the ratio of two blocks of consecutive integers

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      https://www.ias.ac.in/article/fulltext/pmsc/100/02/0107-0132

    • Keywords

       

      Exponential Diophantine equations; elementary Diophantine approximations; linear forms in logarithms; arithmetic-geometric mean

    • Abstract

       

      Under certain assumptions, it is shown that eq. (2) has only finitely many solutions in integersx≥0,y≥0,k≥2,l≥0. In particular, it is proved that (2) witha=b=1, l=k implies thatx=7,y=0,k=3.

    • Author Affiliations

       

      N Saradha1 T N Shorey1

      1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay - 400005
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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