GWD 17-26

[usamiyo]

If n is a positive integer, what is the value of n?
1. When n is divided by 3,the remainder is 2.
2. When n^2 is divided by 3, the remainder is 1.
Ans: E

Why? 我覺得C可求出n值.

[StanleyHuang]

由(1) ==> n=3k+2
由(2) ==> n^2=3m+1
(1)+(2) ==> (3K+2)^2 = 3m+1 ==> 9K^2+12k+4=3m+1
==> 9K^2+12K=3m-3 ==> 3K^2+4K=m-1
當 k=1, m=8 ==> n=5:
K=2, m=21 ==> n=8:
k=3, m=40 ==> 11.......
可以得出一大堆 n，但無法確定n的值，所以選 (E)