Proof that an Even Number Squared is EvenDate: 06/02/99 at 21:03:21 From: Jason Subject: Proof: Even number squared is even How do you prove that any even number squared is even and any odd number squared is odd? For the odd, I let n be the odd number. Then say that n = 2k + 1, so n^2 = 4k^2 + 4k + 1, but from here I am not sure where to go. For the even number I have not gotten very far. Thanks, Jason Date: 06/03/99 at 08:27:12 From: Doctor Rick Subject: Re: Proof: Even number squared is even Hi, Jason. You're practically done. You can factor a 2 out of the first two terms of your expansion: n^2 = 2(2k^2 + 2k) + 1 Since m = 2k^2 + 2k is an integer, you have expressed n^2 as 2m+1, making it odd. The even case is easier: if n = 2k, then n^2 = 4k^2 = 2(2k^2), which is 2 times an integer and therefore is even. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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