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A theorem on approximation of irrational numbers by simple continued fractions

A theorem on approximation of irrational numbers by simple continued fractions

Let ξ be an irrational number with simple continued fraction expansion ξ= [ a 0 ; a 1 , a 2 ,…], P n / q n be its nth convergent, . The following two theorems were proved by Müller [ 9 ] and rediscovered by Bagemihl and McLaughlin [ …