Thread: proof help

a and b are consecutive odd numbers, where a > b.
Prove that a³ - b³ 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 a³ - b³ = (2n + 1)³ - ...............
Expanding the brackets and simplifying,

a³ - b³ = ............+ 2which is 2 more than a multiple of 24, as required.



is b = 2n +1 <a ?

a = 2n+1

b = 2n+3

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'?

my mistake ... so b = 2n-1