On normal numbers
C. E. M. Pearce, Michaël Keane · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1982
Abstract Schmidt has shown that if r and s are positive integers and there is no positive integer power of r which is also a positive integer power of s, then there exists an uncountable set of reals which are normal to base r but not even simply normal to base s. We give a structurally simple proof of this result