Resumen de On digits of Mersenne numbers

Bryce Kerr, László Mérai, Igor E. Shparlinski

• Motivated by recently developed interest to the distribution of q-ary digits of Mersenne numbers Mp=2p−1, where p is prime, we estimate rational exponential sums with Mp, p≤X, modulo a large power of a fixed odd prime q. In turn this immediately implies the normality of strings of q-ary digits amongst about (logX)3/2+o(1) rightmost digits of Mp, p≤X. Previous results imply this only for about (logX)1+o(1) rightmost digits