作者hanabiz (再见 B67)
看板Math
标题Re: [代数] 习题几问
时间Tue Jan 4 12:30:23 2011
※ 引述《jacky7987 (忆)》之铭言：
: 3. If p is a prime and m,n in |N,prove
: pm m
: ( )≡( ) mod p
: pn n
: 先谢谢大家ˊˋ
先来个lemma: suppose char(R) = p, p is prime.
if a,b属於R and ab = ba, then (a+b)^p = a^p + b^p
let R = Z_p[x]
we know char(R) = p (characteristic of R)
(1+x)^(pm) = [(1+x)^p]^m = (1 + x^p)^m 属於 Z_p[x] (by lemma)
consider coefficient of x^(pn)
Q.E.D.
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◆ From: 218.160.249.251
※ 编辑: hanabiz 来自: 218.160.249.251 (01/04 12:45)
1F：推 jacky7987 :问学长一下，char(R)=p是说1要加p个会变成0对吧 01/04 23:03
2F：→ jacky7987 :(偷偷翻了(很)後面的课文) 01/04 23:03
3F：→ hanabiz :原来还没教char喔 我回文简介一下好了 01/04 23:27