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).

Thanks

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- October 14th 2008, 08:46 PMcaptainjapanProofs
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).

Thanks - October 14th 2008, 08:57 PMvincisonfireReply
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.