推 jacky7987 :喔喔雖然考完了不過還是謝謝你:),而且我最後有想到:D 03/29 23:09
※ 引述《jacky7987 (憶)》之銘言:
: Let R be a Eucildean domain with degree fucntion P, and assume that b in R
: is neither zero nor a unit.Prove that for every i≧0, P(b^i)<P(b^{i+1}).
: 我先用degree function 的定義寫下了
: P(b^i)≦P(b^i*b)=P(b^{i+1})
: 然後用提示寫下了
: exists q,r in R such that
: b^i=b^{i+1}*q+r with P(r)<P(b^{i+1})
: 然後就束手無策了
: 感覺只差臨門一腳有誰可以幫我一下嗎?
if r = 0 ,
b^i*1 =b^i*bq => bq=1 ─><─
so r ≠0 ,
P(b^i)≦P((b^i)(1-bq))=P(r)< P(b^{i+1})
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