请教一道余数问题..谢谢

lcommus

if m and n are positive intergers, what is the remainder when 3^(4n+2+m) is divided by 10

1) n=2
2) m=1

answer B

[此贴子已经被作者于2009/10/26 22:00:17编辑过]

lcommus

if p and n are positive intergers,and p>n,what is the remainder when p^2-n^2 is divided by 15?

1) the remainder when p+n is divided by 5 is 1
2) the remainder when p-5 is divided by 3 is 1

answer: E 但我觉得是C.求讨论

lcommus

再来一题，都是PREP破解上的题目，发现同类问题都不会做，有没有大牛指导一下方法

If p is a positive odd interger,what is the remainder when p is divided by 4?

1) when p is divided by 8, the remainder is 5
2) p is the sum of squares of tow positive intergers.

答案是D.对于2）怎么成立的不会算。

firstfengrui

以下是引用lcommus在2009/10/26 21:17:00的发言：
if m and n are positive intergers, what is the remainder when 3^(4n+2+m) is divided by 10

1) n=2
2) m=1

answer B

1）3^10+m，  因为m不确定，所以不知余数

2）3^4n+3       因为3^n 除以10分别为3.9.7.1.  所以不管n的取值为多少，都是余数为7

sunnygirl_jj

p is odd number, so it must be the sum of one odd number sqaure and one even number square

p = (n+1) ^ 2 + m ^ 2, both n and m are even numbers

p = n ^ 2 + 2n + 1 + m ^ 2

Because both n and m are even numbers, n^2, 2n and m^2 can all be divided by 4

Thus the remainder is 1.