Prep11，不知道（2）是怎么回事啊~求解答！谢谢~

lovepunch

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.

答案是D，我不知道（2）怎么做？求牛人解答~万分感谢！

sdcar2010

P = odd  What is the remainder when p is divided by 4?

(2) p = m^2 + k^2, Since p is odd, then m^2 and k^2 is one odd and one even. Let's assume m^2 is even, then m^2 has to have 4 as a factor. If k^2 is odd, then k^2 = (2*q + 1)^2 = 4*q^2 + 4*q +1

So when p is divided by 4, the remainder is 1.

lovepunch

精辟！到位！thanks~~~~