Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

A theorem on approximation of irrational numbers by simple continued fractions

Jingcheng Tonga1a2

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, S001309150000331X_inline2. The following two theorems were proved by Müller [9] and rediscovered by Bagemihl and McLaughlin [1]:

Theorem 1.For n>1, S001309150000331X_inline1

(Received April 16 1986)