推 jacky7987 :問學長一下，char(R)=p是說1要加p個會變成0對吧 01/04 23:03
→ jacky7987 :(偷偷翻了(很)後面的課文) 01/04 23:03
→ hanabiz :原來還沒教char喔 我回文簡介一下好了 01/04 23:27
※ 引述《jacky7987 (憶)》之銘言：
: 3. If p is a prime and m,n in |N,prove
: pm m
: ( )≡( ) mod p
: pn n
: 先謝謝大家ˊˋ
先來個lemma: suppose char(R) = p, p is prime.
if a,b屬於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 屬於 Z_p[x] (by lemma)
consider coefficient of x^(pn)
Q.E.D.
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◆ From: 218.160.249.251
※ 編輯: hanabiz 來自: 218.160.249.251 (01/04 12:45)