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标题: 请教思路prep２ [打印本页]

作者: butterfly08 时间: 2007-12-13 20:07
标题: 请教思路prep２
54. When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. what is the remainder when the product nt is divided by 15?

1) n-2 is divisible by 5 2) t is divisible by 5

Answer: C

作者: mktkang 时间: 2007-12-15 09:31

条件２　和　题干怎么说ｔ不同啊。

作者: butterfly08 时间: 2007-12-15 22:04

哦条件2错了应该是 t is divisible by 3

请再帮看看吧谢谢

作者: atc 时间: 2007-12-15 22:08

此题关键是如何写出满足题意的通项

对于integer n is divided by 3, the remainder is 2，有N=3X+2

positive integer t is divided by 5, the remainder is 3，有T=5Y+3

对于条件1) n-2 is divisible by 5 ，关键是如何写出满足条件的通项

N也可以写成N=15X+2，+5，+8，+11，+14只有N=15X+2满足题意，

同理，T=15Y+3

结合1）2），可得余数为6

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