a1 Department of Mathematical Sciences, University of North Florida, Jacksonville, FL 32216, U.S.A.
a2 Institute of Applied Mathematics, Academia Sinica, Peking, China
Let ξ be an irrational number with simple continued fraction expansion ξ= [a0;a1,a2,…], Pn/qn be its nth convergent, . The following two theorems were proved by Müller  and rediscovered by Bagemihl and McLaughlin :
Theorem 1.For n>1,
(Received April 16 1986)