prep-1-11

yalemba

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.

 答案：D

 怎么觉得是 A

 （2）怎么推出来呢

xiaoxiugirl

特殊值

vincentwh

p is the sum of the squares of two positive integers

-> must be sum of the squares of an odd number and an even number (p is a positive odd integer)

-> p=(2m)^2+(2n+1)^2=4m^2+4n^2+4n+1=4(m^2+n^2+n)+1