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# Need proof (2)

Let m>2. {0^2, 1^2, ... ,(m-1)^2} must not be a complete set of residues modulo m.

### 1 Answer

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- ☂雨後晴空☀Lv 78 years agoFavorite Answer
If d ∈ (1,2,3,...m-1)

then (m - d) ∈ (1,2,3,...m-1)For m>2 , exist some d for d ≠ m - d. Consider

(m - d)²

≡ m(m - 2d) + d²

≡ d² (mod m)So {0² , 1² , ... ,(m-1)²} must not be a complete set of residues modulo m.

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