YLL討論網

txreformer 寫到:#ed_op#div#ed_cl##ed_op#strong#ed_cl#2.#ed_op#/strong#ed_cl# 有一個數，除以7餘2，除以8餘4，除以9餘3，這個數是多少？#ed_op#/div#ed_cl#

#ed_op#br#ed_cl#第二題另另解：#ed_op#br#ed_cl#先算"除以7餘2，除以8餘4" 由於此數除以8餘4，故為雙數，而且減去2後為7的倍數#ed_op#br#ed_cl#=> 盡列7*少於7的雙數的情況：#ed_op#br#ed_cl#7*2 +2-4 = 12 (不是8的倍數),#ed_op#br#ed_cl#7*4 +2-4 = 26 (不是8的倍數),#ed_op#br#ed_cl#7*6 +2-4 = 40 (是8的倍數) => 故此數除以7*8=56餘40+4=44;#ed_op#br#ed_cl#題目變成：有一個數，除以56餘44，除以9餘3；#ed_op#br#ed_cl#盡列56*少於9的情況：#ed_op#br#ed_cl#56*0+44-3 = 41 (不是9的倍數),#ed_op#br#ed_cl#56*1+44-3 = 97 (不是9的倍數),#ed_op#br#ed_cl#56*2+44-3 = 153 (是9的倍數) => 這個數除以56*9=504餘153+3=156;#ed_op#br#ed_cl#此數為504n+156, n為自然數。#ed_op#br#ed_cl#

zxc 寫到:請問mod的定義?#ed_op#br#ed_cl##ed_op#br#ed_cl##ed_op#br#ed_cl#請問mod的定義?

#ed_op#br#ed_cl#餘數... e.g. 5%3=2, 6543%10=3#ed_op#br#ed_cl#不好意思...沒有留意這是國小的問題....用了深奧的解法.....#ed_op#br#ed_cl#

請問mod的定義?


請問mod的定義?

txreformer 寫到:#ed_op#div#ed_cl##ed_op#strong#ed_cl#2.#ed_op#/strong#ed_cl# 有一個數，除以7餘2，除以8餘4，除以9餘3，這個數是多少？#ed_op#/div#ed_cl#

#ed_op#br#ed_cl#第二題另解：#ed_op#br#ed_cl#設 8*9*i = 2 (mod 7);  7*9*j = 4 (mod 8);  7*8*k = 3 (mod 9) => i=1, j=4, k=6;#ed_op#br#ed_cl#8*9*i + 7*9*j + 7*8*k = 72+252+336 = 156 (mod 7*8*9)#ed_op#br#ed_cl#此數為 504n+156, n∈#ed_op#span style="font-weight: bold; font-style: italic;"#ed_cl#N#ed_op#/span#ed_cl##ed_op#br#ed_cl##ed_op#br#ed_cl#

又在打最後一句時按錯了制.....懊惱極了....#ed_op#br#ed_cl##ed_op#br#ed_cl#

txreformer 寫到:#ed_op#div#ed_cl##ed_op#strong#ed_cl#1.#ed_op#/strong#ed_cl# 582除以一個數，所得之不完全商為11，並且除數與餘數的差為6，請問除數、餘數各是多少？#ed_op#/div#ed_cl##ed_op#div#ed_cl#

#ed_op#br#ed_cl#設餘數為x, 除數即為x+6 [註：除數必大於餘數]#ed_op#br#ed_cl#582 = 11(x+6) + x = 12x + 66  >  x = 43; x+6 = 49#ed_op#br#ed_cl##ed_op#br#ed_cl##ed_op#/div#ed_cl##ed_op#div#ed_cl#

txreformer 寫到:#ed_op#br#ed_cl##ed_op#strong#ed_cl##ed_op#/strong#ed_cl##ed_op#strong#ed_cl#2.#ed_op#/strong#ed_cl# 有一個數，除以7餘2，除以8餘4，除以9餘3，這個數是多少？#ed_op#/div#ed_cl##ed_op#div#ed_cl#

#ed_op#br#ed_cl#設 8*9*i = 1 (mod 7);  7*9*j = 1 (mod 8);  7*8*k = 1 (mod 9) => i=4, j=7, k=5;#ed_op#br#ed_cl#8*9*i *2 + 7*9*j *4 + 7*8*k *3 = 576+1764+840 = 156 (mod 7*8*9)#ed_op#br#ed_cl#此數為 504n+156, n∈#ed_op#span style="font-weight: bold; font-style: italic;"#ed_cl#N#ed_op#/span#ed_cl##ed_op#br#ed_cl##ed_op#br#ed_cl##ed_op#/div#ed_cl#

txreformer 寫到:#ed_op#br#ed_cl##ed_op#strong#ed_cl##ed_op#/strong#ed_cl##ed_op#strong#ed_cl##ed_op#/strong#ed_cl##ed_op#div#ed_cl##ed_op#strong#ed_cl#3.#ed_op#/strong#ed_cl# 63285和70352的積除以7，餘數是多少？#ed_op#/div#ed_cl##ed_op#div#ed_cl#

#ed_op#br#ed_cl#63285 = 5 (mod 7); 70352 = 2 (mod 7); [註：63,28,7,35皆為7之倍數，數此二數能速算出]#ed_op#br#ed_cl#5*2 = 10 = 3 (mod 7)  =>  餘數為3#ed_op#br#ed_cl##ed_op#br#ed_cl##ed_op#/div#ed_cl#

txreformer 寫到:#ed_op#br#ed_cl##ed_op#strong#ed_cl##ed_op#/strong#ed_cl##ed_op#strong#ed_cl##ed_op#/strong#ed_cl##ed_op#div#ed_cl##ed_op#strong#ed_cl#4.#ed_op#/strong#ed_cl# 陽曆1992年1月1日是星期三，陽曆2004年1月1日是星期幾？#ed_op#/div#ed_cl##ed_op#div#ed_cl#

#ed_op#br#ed_cl#2004年-1992年 = 12年; 12年有12/4=3個閏年; 1年有 365日=52星期+1日;#ed_op#br#ed_cl#12*1 + 3 = 15 = 1 (mod 7);  故 2004年1月1日為星期三+1=星期四#ed_op#br#ed_cl##ed_op#br#ed_cl##ed_op#/div#ed_cl#

txreformer 寫到:#ed_op#br#ed_cl##ed_op#strong#ed_cl##ed_op#/strong#ed_cl##ed_op#strong#ed_cl##ed_op#/strong#ed_cl##ed_op#div#ed_cl##ed_op#strong#ed_cl#5.#ed_op#/strong#ed_cl# 甲乙丙丁玩報數，甲報1；乙報2；丙報3；丁報4；丙報5；乙報6；甲報7；乙報8... ...，報2003這數的為誰？#ed_op#/div#ed_cl##ed_op#div#ed_cl##ed_op#br#ed_cl# 本席算是乙 ，不知對不對#ed_op#br#ed_cl#

#ed_op#br#ed_cl#2003 = 5 (mod 2*(4-1)) => 5為丙報#ed_op#br#ed_cl#故乙為不對...#ed_op#br#ed_cl##ed_op#/div#ed_cl#

#ed_op#DIV#ed_cl##ed_op#STRONG#ed_cl#1.#ed_op#/STRONG#ed_cl# 582除以一個數，所得之不完全商為11，並且除數與餘數的差為6，請問除數、餘數各是多少？#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#STRONG#ed_cl#2.#ed_op#/STRONG#ed_cl# 有一個數，除以7餘2，除以8餘4，除以9餘3，這個數是多少？#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#STRONG#ed_cl#3.#ed_op#/STRONG#ed_cl# 63285和70352的積除以7，餘數是多少？#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#STRONG#ed_cl#4.#ed_op#/STRONG#ed_cl# 陽曆1992年1月1日是星期三，陽曆2004年1月1日是星期幾？#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#STRONG#ed_cl#5.#ed_op#/STRONG#ed_cl# 甲乙丙丁玩報數，甲報1；乙報2；丙報3；丁報4；丙報5；乙報6；甲報7；乙報8... ...，報2003這數的為誰？#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#本席算是乙 ，不知對不對#ed_op#/DIV#ed_cl#