On the Powers of Some Transcendental Numbers
On the Powers of Some Transcendental Numbers
We construct a transcendental number α whose powers α n! , n = 1, 2, 3,…, modulo 1 are everywhere dense in the interval [0, 1]. Similarly, for any sequence of positive numbers δ = (δ n ) ∞ n=1 , we find a transcendental number α = α(δ) such …