Need proof (2)
2012-08-05 12:10 am
Let m>2. {0^2, 1^2, ... ,(m-1)^2} must not be a complete set of residues modulo m.
回答 (1)
2012-08-05 2:19 am
✔ 最佳答案
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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