On the simple normality to base 2 of the square root of s, for s not a perfect square
Abstract
Description
We show that each number of the form, the square root of s for s not a perfect square, is simply normal to the base 2. The argument uses some elementary ideas from the calculus of finite differences.
14 pages; Lemma 6 of the original version is incorrect. This revision provides an alternative argument to get the desired result. Except for minor modifications, the revision agrees with the original through and including lemma 4. The alternative argument begins in the revision after the conclusion of Lemma 4. Additional modifications include correction of a few typos, rephrasing of some exposition, and the clarification of confusing notation for the partial difference on p. 7
14 pages; Lemma 6 of the original version is incorrect. This revision provides an alternative argument to get the desired result. Except for minor modifications, the revision agrees with the original through and including lemma 4. The alternative argument begins in the revision after the conclusion of Lemma 4. Additional modifications include correction of a few typos, rephrasing of some exposition, and the clarification of confusing notation for the partial difference on p. 7