求助一道简单的GWD题目，求解题思路

camelo777

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.

rontsai

I got E
(1) we only know n=3p+2, p∈Z, p＞0, insuff
(2) we only know n^2=3q+1, q∈Z, q＞0, insuff
(1)+(2), we know (3p+2)^2=3q+1, 3q=(3p+2)^2－1^2=(3p+3)(3p+1),
so  q＝(p+1)(3p+1),
let p be 0, then q=1, n=2；
let p be 1, then q=8, n＝5；insuff

camelo777

thanks , i got it now