求教 prep ds 1- 11, 16

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

16.  Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

 (1) Lines n and p intersect at the point (5,1).

(2) The y-intercept of line n is greater than the y-intercept of line p.

答案C

不明白啊 大家帮帮我！谢谢！

16.单独看1.2肯定不可以，举个反例很容易证明。

合在一起考虑：假如他们在y轴上的交点分别是（0，n）（0，p），已知n>p,intersect(5,1)

the slope of line n is 1-n)/5

the slope of line p is1-p)/5

because n>p,so (1-n)<(1-p)=>the slope of line n is less than the slope of line p.

15.

1).令p=8n+5,when p is divided by 4,p/4=2n+5/4=>obviously the remainder is 1.

2).令p=a2+b2,because p is odd.a b必定是一奇一偶，然后俺就是用笨方法了，1-10内任何一奇一偶的平方和被4除后余数都是1.

呵呵，it is not a smart solution and seemingly not convincing. Hope smart guys provide persuasive solution. 

第15题受到NN的启发。

令p=a^2+b^2,because p is odd.a b必定是一奇一偶 令a=2k,b=2k+1,a^2=4k^2可以被4整除，

b^2=(2k+1)^2=4k^2+4k+1,所以除以四的时候余数是1.heh

谢谢楼上！我懂啦！