範例 08:a的n次方首位數字  
 

 

 
  《 解答 》  
 

Problem:

and set .

We want to prove that

Definition:

Lemma:

Proof:,
if , .(→←)

Theorem:has uniform distribution in (0,1).

見Hardy and Wright, An Introduction to the Theory of Numbers. P390, 定理445.

 
 
 
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