Products of Integers (Even or Odd)Date: 03/23/2002 at 14:48:31 From: Kristine Hodges Subject: Product of two even integers proof How can I prove that the product of two even integers is an even integer? And that the product of two odd integers is an odd integer? I know that it is true, but I don't know how to put it in an equation. Thanks. Kristine Hodges Date: 03/23/2002 at 15:13:23 From: Doctor Paul Subject: Re: Product of two even integers proof Let x and y be even numbers. Then x = 2*a and y = 2*b for some integers a and b. Then x*y = 2*(2*a*b), which is even. Now let x and y be two odd numbers. Any odd number is always one more than some even number. Thus we can write x = 2*a + 1 and y = 2*b + 1 for some integers a and b. Then x*y = (2*a + 1) * (2*b + 1) = 4*a*b + 2*a + 2*b + 1 = 2(2*a*b + a + b) + 1, which is one more than an even number and is hence odd. I hope this helps. Please write back if you'd like to talk about this some more. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/ |
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