[理工] [離散] 整係數方程式

看板Grad-ProbAsk作者 (Larry)時間11年前 (2012/09/17 23:23), 編輯推噓6(6推 0噓 5→)
留言11則, 4人參與, 最新討論串1/1
True of False: 1.Let n be a fixed positive integer that satisfies the property: For all a,b∈Z+, if n|ab then n|a or n|b. Then n=1 or n is prime. 2.With gcd(a,b)=1, if a|c and b|c are true, then ab|c is true. Show the following: 1.gcd(m,n) is a divisor of n-m. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 123.192.157.110
推
09/18 00:47, , 1F
1.T 2.F 令gcd(m,n)=d, d|m,d|n 故d|n-m
09/18 00:47, 1F
→
09/18 10:23, , 2F
第一題true怎麼推導? 還有第二題是true喔
09/18 10:23, 2F
推
09/18 11:32, , 3F
看漏gcd(a,b)=1了... 1. 證 p->q = 證 ~q -> ~p
09/18 11:32, 3F
→
09/18 11:33, , 4F
設n非1or質數,則n=xy for some x,y=/=1,此時令a=x,b=y得矛盾
09/18 11:33, 4F
推
09/18 11:38, , 5F
2.gcd(a,b)=1,故a,b最小公倍數是ab,又a|c,b|c ,c是a,b之
09/18 11:38, 5F
→
09/18 11:39, , 6F
公倍數為最小公倍數ab之倍數,故ab|c
09/18 11:39, 6F
推
09/18 22:43, , 7F
令gcd(m,n)=k,k|m&k|n,令m=p*k,n=q*k(p,q∈Z),欲證k|n-m
09/18 22:43, 7F
→
09/18 22:44, , 8F
->k|(q*k-p*k)->k(q-p),故k|n-m
09/18 22:44, 8F
推
09/18 22:58, , 9F
阿沒看到樓上已經解了XD
09/18 22:58, 9F
推
09/27 01:58, , 10F
可是第一題假如說代數字進去 a=6 b=12 n=6
09/27 01:58, 10F
→
09/27 01:58, , 11F
這樣答案是F吧? 還是我題目有看漏的?
09/27 01:58, 11F
‣ 更多 movo11 的文章
文章代碼(AID): #1GLq25T_ (Grad-ProbAsk)