Sums of Odd and Even NumbersDate: 02/04/2002 at 20:30:37 From: Megs Subject: Odd and Even numbers I have to prove why the sum of two even numbers is an even number, and why the sum of an even and an odd number is an odd number. I've tried using the variable "n" as an odd number, but I don't understand where to go from there. Thanks. Date: 02/04/2002 at 22:28:46 From: Doctor Paul Subject: Re: Odd and Even numbers Let x and y be even numbers. Then x = 2*k and y = 2*m for some integers k and m. Then x+y = 2*k + 2*m = 2*(k+m) which is a multiple of two, and hence is even. Now suppose x is even but y is odd. Then x = 2*k and y = 2*m + 1 for some integers k and m. Then x+y = 2*k + 2*m + 1 = 2*(k+m) + 1 which is one more than a multiple of two and hence is odd. 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/ Date: 02/08/2002 at 23:10:19 From: Megs Subject: Odd and Even numbers Your help on my problem helped immensely. Thank you very, very much! Megan |
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