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Math Help - Proofs

  1. #1
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    Proofs

    a) Prove that if n is a perfect square, then n + 2 is not a perfect square.

    b) Use a proof by cases to show that min(a, min(b, c)) = min(min(a, b), c).

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  2. #2
    Senior Member vincisonfire's Avatar
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    Reply

    a) if n is a perfect square, is has form 4b or 4b+1.
    Let n = a^2.
    If a=2k (even) then n = 4(k^2) = 4b.
    If a=2k+1 (odd) then n= 4k^2+4k+1 = 4(k^2+k) + 1 = 4b+1.
    4b + 2 and 4b+3 are not of these form and it is thus impossible that they are perfect square.
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