Question

Prove that the square of any positive integer is of the 3m or 3m+1 but not of the form 3m+2

Answer 1

hello :
prove : n²≡0 (mod 3) or n²≡1 (mod 3)...no n²≡2 (mod 3)
1 ) n ≡ 0 (mod 3)....(1)
n² ≡ 0 (mod 3)
2) n ≡ 1 (mod 3)....(2)
n² ≡ 1 (mod 3)
3 ) n ≡ 2 (mod 3)....(3)
n² ≡ 4 (mod 3) but : 4≡ 1 (mod 3)
so : n² ≡ 1 (mod 3)