Prove that out of two consecutive integers, one is divisible by 2
Hi. I'm supposed to prove that given any two consecutive integers a and a+1, one of them is divisible by 2. And I'm supposed to use the Division Algorithm. I'm not entirely sure where to begin.
Re: Prove that out of two consecutive integers, one is divisible by 2
Originally Posted by oregongirl
Hi. I'm supposed to prove that given any two consecutive integers a and a+1, one of them is divisible by 2. And I'm supposed to use the Division Algorithm. I'm not entirely sure where to begin.
Any help is appreciated!
suppose a is divisible by 2. You're done.
suppose a is not divisible by 2. Then a = 2k + 1 for some k (i.e. a is an odd number)
then a + 1 = (2k+1) + 1 = 2k + 2 = 2(k+1) and thus (a+1) is divisible by 2