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

Question

Mathematics

Elsie Haynes

24 June, 08:55

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

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Alisson Robles · 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)