On digits of Mersenne numbers
Bryce KerrMax Planck Institute for Mathematics, Bonn, Germany
László MéraiAustrian Academy of Sciences, Linz, Austria
Igor E. ShparlinskiUniversity of New South Wales, Sydney, Australia
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. 1901–1925DOI 10.4171/RMI/1316