Derek asked in 科學及數學數學 · 7 years ago

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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  • 7 years ago
    Best 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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