
proof help
a and b are consecutive odd numbers, where a > b.
Prove that a^{3}  b^{3} is 2 more than a multiple of 24.
Fill in the gaps in the following proof.
a is odd, so a = 2n+1 for some integer n.
Then in terms of n, b =..............
so a^{3}  b^{3} = (2n + 1)^{3}  ...............
Expanding the brackets and simplifying,
a^{3}  b^{3} = ............+ 2which is 2 more than a multiple of 24, as required.
is b = 2n +1 <a ?

Re: proof help

Re: proof help
Quote:
Originally Posted by
skeeter a = 2n+1
b = 2n+3
Thank you, but 'b' is less than 'a', so I dont understand how it can be 2n+3?, that would mean b is always going to be a bigger odd number than 'a'?

Re: proof help
my mistake ... so b = 2n1