P
分数如果表成--- (N,P)=1 若将分数化为小数,循环节最多N-1位
N
请问证明如何写会比较清楚明了?
作者: JohnMash (Paul) 看板: Math
※ 引述《gary85238 (小黄)》之铭言：
: Let a,b 属於 N , a<b and a is relative prime to b.
: Use the Pigeonhole Principle to show that the decimal representation
: of the fraction a/b either terminate or repeats.
if a/b terminates in its representation, done.
if a/b does not terminate
consider a, 10a, 100a, ....,10^b a,....
a=a_0 (mod b)
10a=a_1 (mod b)
100a=a_2 (mod b)
......
because a_0,a_1,a_2,...,a_b are all less than b
then there exist at least two a_i, a_j equal
that is 10^i a= kb+10^j a
10^i a/b=k+10^j a/b
that is 10^i a/b has the same decimal part as 10^j a/b
it means a/b repeats its decimal representation
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◆ From: 112.104.114.234
1F：推 ATOU0526 :多谢不过有人可以帮忙翻译一下吗?原文已经离我太遥远 04/26 12:04
2F：→ BARGARYARLOO:写这样已经很清楚了吧 自己查字典比较快 04/26 14:25
※ 编辑: JohnMash 来自: 112.104.144.227 (04/26 18:00)