請幫忙解解下列題目:
A three-digit number N leaves remainder 3 when divided by 7, remainder 5 when divided by 11 and remainder 8 when divided by 17. What is the number N?

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2005-10-10 21:50
N / 7 =? .........3
N / 11 =?...........5
N / 17 =?...........8


請用孫子算法?再想想看! 我也再算........

sam

2005-10-10 22:23
先把11, 17公倍數
11 x 17 = 187, 187/7=26...5 ( 5不是他們要的,而是3)
5 x 2 =10 10/7=1.....3,
所以 11 x 17 x 2 = 374
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7, 17公倍數
7 x 17 = 119, 119/11=10...9
9 x 3 = 27, 27/11=2...5,
所以17x 7 x 3 = 357
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11, 7公倍數
11 x 7 = 77, 77/17=4.......9
9 x 16 = 144 , 144/17=8 ....8
所以 7 x 11 x 16= 1232
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1232 + 374 + 357 = 1963

1963 - N的公倍數
所以11x 7x 17= 1309(N的公倍數)
1963-1309=654

所以三位數是654

Ans:654

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不知我寫您看懂否?

sam



2005-10-11 00:01
辛苦你了! 謝謝

2005-11-28 15:37
從另一個角度看題:由3算起加7的倍數:3,10,17,24,31,38----;由5起算加11的倍數:5,16,27,38--;共同最小數為38;自38起加77的倍數:38,115,192,269,346,423,500,577,654(所求) 

2005-12-01 09:56
提示:請考慮2N+1

2006-02-19 23:06
我英文極為不好誰能幫我翻譯一下~_~