If n^2 is Even, n is Even
Date: 02/21/2002 at 23:42:26 From: Mary Jackson Subject: Show that n^2 is even then n is even. I have to show that if n^2 is even then n is also even. I don't know where to start. I would love your help. Thanks.
Date: 02/22/2002 at 00:45:20 From: Doctor Paul Subject: Re: Show that n^2 is even then n is even. Try a proof by contraposition (are you familiar with this method of proof? a statement and its contrapositive are logically equivalent so proving the contrapositive of the original statement actually proves the original statement). So what you want to do is assume that n is not even (i.e., it is odd) and show that n^2 is not even (i.e., it is odd). n is odd means that you can write n = 2*k + 1 for some integer k. Then n^2 = 4*k^2 + 4*k + 1 = 2 * (2*k^2 + 2*k) + 1 which is clearly odd. This completes the proof. I hope this helps. Please write back if you'd like to talk about this more. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/
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