On digits of Mersenne numbers

  • Bryce Kerr

    Max Planck Institute for Mathematics, Bonn, Germany
  • László Mérai

    Austrian Academy of Sciences, Linz, Austria
  • Igor E. Shparlinski

    University of New South Wales, Sydney, Australia
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Motivated by recently developed interest to the distribution of -ary digits of Mersenne numbers , where is prime, we estimate rational exponential sums with , , modulo a large power of a fixed odd prime . In turn this immediately implies the normality of strings of -ary digits amongst about rightmost digits of , . Previous results imply this only for about rightmost digits.

Cite this article

Bryce Kerr, László Mérai, Igor E. Shparlinski, On digits of Mersenne numbers. Rev. Mat. Iberoam. 38 (2022), no. 6, pp. 1901–1925

DOI 10.4171/RMI/1316