tag:blogger.com,1999:blog-3550204829234352390.post8873276374024637137..comments2024-03-27T09:13:48.546+08:00Comments on 研發養成所 ( Bridan's Blog - 4rdp, For R&D Person ): 訓練數學感 160 ─ 正因數有多少個?Bridanhttp://www.blogger.com/profile/17055047757114667099noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-3550204829234352390.post-85234407492145551602018-01-18T22:23:41.760+08:002018-01-18T22:23:41.760+08:00嗯,說得也是,不過有興趣的人還是可以想看看。嗯,說得也是,不過有興趣的人還是可以想看看。Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-89253791611395843772018-01-18T19:48:19.982+08:002018-01-18T19:48:19.982+08:00哈哈,奇奇怪怪的函數還有很多呢。哈哈,奇奇怪怪的函數還有很多呢。.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-73653121039269317192018-01-18T18:32:07.476+08:002018-01-18T18:32:07.476+08:00西瓜謝謝你的詳解,已把標題修正,避免誤會。
從這個題目給我一個靈感,目前加密是以極大質數處理,總有一...西瓜謝謝你的詳解,已把標題修正,避免誤會。<br />從這個題目給我一個靈感,目前加密是以極大質數處理,總有一天這極大質數會有方法處理,或許可以再加入因數數量計算,增加電腦計算量來加強保護。Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-25146322946734975992018-01-18T17:48:38.686+08:002018-01-18T17:48:38.686+08:00我會問是因為題意不清,因數總數,我認為是有包含負因數的。不過,高一前是不討論啦。我會問是因為題意不清,因數總數,我認為是有包含負因數的。不過,高一前是不討論啦。.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-58615315189874088812018-01-18T17:46:34.316+08:002018-01-18T17:46:34.316+08:00(LaTeX編輯)
令N有n個質因數(ω(N)=n),且標準分解式
N=2^{a_{1}}\tim...(LaTeX編輯)<br /><br />令N有n個質因數(ω(N)=n),且標準分解式<br />N=2^{a_{1}}\times3^{a_{2}}\times5^{a_{3}}\times...\times p_{n}^{a_{n}}<br />其中p_{i}為第n個質因數,a_{i}為p_{i}經過的冪次。<br /><br />根據正因數個數的計算公式<br />d(2N)=(a_{1}+2)(a_{2}+1)(a_{3}+1)...(a_{n}+1)=28<br />d(3N)=(a_{1}+1)(a_{2}+2)(a_{3}+1)...(a_{n}+1)=30<br />上下相除。<br />\frac{d(2N)}{d(3N)}= \frac{(a_{1}+2)(a_{2}+1)}{(a_{1}+1)(a_{2}+2)}=\frac{28}{30}=\frac{14}{15}<br />交叉相乘後強迫因式分解。<br />15(a_{1}+2)(a_{2}+1)=14(a_{1}+1)(a_{2}+2)<br />a_{1}a_{2}-13a_{1}+16a_{2}+2=0<br />(a_{1}+16)(13-a_{2})=210<br /><br />顯然兩個括號都是正的,因此探討210的正因數。<br />210=210\times1=105\times2=70\times3=42\times5=35\times6=30\times7=21\times10=15\times14=...<br />其餘的右乘項會大於左乘項,而a_{1}+16\geq 16>13\geq 13-a_{2},不合。<br /><br />計算得<br />a_{1}=194\vee 89\vee 54\vee 26\vee 19\vee 14\vee 5\vee -1(-1不合。)<br />對應的a_{2}=12\vee 11\vee 10\vee 8 \vee 7 \vee 6\vee 3\vee -1 (-1不合。)<br />又由d(2N)及d(3N)可知,a_{1}+2,a_{2}+1為28的因數;a_{1}+1,a_{2}+2為30的因數,將不合者再次剔除,因此<br />a_{1}=5<br />對應的a_{2}=3<br />代回原式<br />d(2N)=(7\times4)(a_{3}+1)...(a_{n}+1)=28<br />d(3N)=(6\times5)(a_{3}+1)...(a_{n}+1)=30<br />得知後面那一串都是1,因此<br />a_{3}=a_{4}=a_{5}=...a_{n}=0<br />由此可知N=2^{5}\times3^{3}=864。<br /><br />N=864,唯一解。<br />.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-26623110364120110652018-01-17T21:32:18.343+08:002018-01-17T21:32:18.343+08:00祝考試順利,期待你的答案。祝考試順利,期待你的答案。Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-49910730034286300602018-01-17T21:16:14.119+08:002018-01-17T21:16:14.119+08:00是的!詳細過程明天段考後會貼上來。是的!詳細過程明天段考後會貼上來。.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-76105451492836576002018-01-17T19:46:44.691+08:002018-01-17T19:46:44.691+08:00孫老師以程式暴力破解,解答在 http://4rdp.blogspot.tw/2018/01/ros...孫老師以程式暴力破解,解答在 http://4rdp.blogspot.tw/2018/01/rosa-46-otto-like.html?showComment=1516167491037#c6851653993359769098<br /><br />加分題,這是唯一解嗎?Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-5080128094653895522018-01-17T09:06:36.831+08:002018-01-17T09:06:36.831+08:00是的。是的。Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-68647127597191710052018-01-16T23:10:57.665+08:002018-01-16T23:10:57.665+08:00是否為"正因數個數"?是否為"正因數個數"?.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-70068173113177110312018-01-15T20:08:02.440+08:002018-01-15T20:08:02.440+08:00已經補充內文加入舉例,希望老師能夠理解。已經補充內文加入舉例,希望老師能夠理解。Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-1697365789618636942018-01-15T16:48:35.692+08:002018-01-15T16:48:35.692+08:00“它2的倍數有28個因數”這句沒看懂。可以解釋一下嗎?“它2的倍數有28個因數”這句沒看懂。可以解釋一下嗎?flyingdustshttps://www.blogger.com/profile/10543166743971149568noreply@blogger.com