Prep DS1-11 平方和相加会和4整除有关系？

yifengjingyus

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. 不明白 （2）怎么可以推出来，请高手指点，谢谢。

yifengjingyus

Good. Thank you .

yifengjingyus

i got it,thanks !!!

primefangs

nod!

bloomingtrees

题目说p是奇数，又是两个整数的平方和，那只能是一个偶数的平方加上一个奇

数的平方。所有正偶数的平方都能被4整除，所有奇数的平方除4都余1，（2）推出p

被4整除余1