prep1-11

LilyJune

 

11.  

If p is a positive odd integer, 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 the squares of two positive integers.

由条件2也能推出？

怎么考虑的？

谢谢

CasualWalker

如果2对的话,而p是奇数 ,那么p可以写成如下形式：

p= (2a+1)^2+ (2b)^2

a,b地位等同，可以互换

所以p=4*a^2+4*a+1+4*b^2

所以余数是1

LilyJune

many thanks!!