有一道gwd数学难题啊，急！

wmh1016

A school administrator will assign each student in a group of n students to one of m classrooms.  If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?

(1)   It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.

(2)   It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.

会的兄弟姐妹帮帮忙阿，万分感谢

happyfish0517

请在题目中注明题号及题目来源...谢谢合作！！

harrischen

条件1中的3N和M不互质,所以不充分,例如N=14,M=3

条件2中的13N和M互质,所以充分.选B

supermonkey

以下是引用harrischen在2005-8-8 8:31:00的发言：

条件1中的3N和M不互质,所以不充分,例如N=14,M=3

条件2中的13N和M互质,所以充分.选B

没看懂。。。能不能解释下。。。谢谢。

harrischen

题目问N能平均分配到M个班级吗?

条件1.3N能平均分配到M个班级 由于3<M<13,并不代表N能被M整除,反例 N=14,M=3

条件2.13N能平均分配到M个班级,由于3<M<13,所以13和M互质,所以N能平均分配到M个班级.选B