283. 有5个整数a1,a2,a3,a4,a5，这5个数除以5的余数都不相同。问下列哪几组数除以5的余数也都各不相同。

leeguoyan

283. 有5个整数a1,a2,a3,a4,a5，这5个数除以5的余数都不相同。问下列哪几组数除以5的余数也都各不相同。
a) a1+2, a2+2,..., a5+2
b) 2*a1, 2*a2,..., 2*a5
c) a1^2, a2^2,..., a5^2

E???

liyang229

first, lets assume the there are five numbers
a1,a2,a3,a4,a5.  with a reminder 0,1,2,3,4. these are the only five reminders that FIVE could have.
thus, when a1+2,a2+2......a5+2. divide by 5. the reminder will become 2,3,4,0,1. So, the reminder is also unique.

and for2*a1, 2*a2,..., 2*a5,
it will be  0,2,4,1,3. which is also unique.

and for a1^2, a2^2,..., a5^2.
it will be  1,4,4,1,0. which is not unique.

so, the answer is A and B.

leeguoyan

thanks a lot