For any irrational number a show that the fractional parts of an, which is denoted by {an), are uniformly distributed in the interval [0, 1].

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For any irrational number a show that the fractional parts of an, which is
denoted by {an), are uniformly distributed in the interval [0, 1].
The above two are due to Callahan (1964). His argument is very simple be-
cause he makes use neither of continued fractions or of exponential sums.
Transcribed Image Text:For any irrational number a show that the fractional parts of an, which is denoted by {an), are uniformly distributed in the interval [0, 1]. The above two are due to Callahan (1964). His argument is very simple be- cause he makes use neither of continued fractions or of exponential sums.
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