• On the ratio of two blocks of consecutive integers

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    • 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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