Help!:

Prove by contradiction. If a,b and c are consecutive integers s.t. a<b<c then a^3 + b^3 /=/ c^3 (Cannot equal to c^3).

Here are my steps... let me know if I am on the right track:

For the sake of contradiction: a^3 + b^3 = c^3

(at this point, a<b<c would still hold right?

It is the problem to find a^3 + b^3 = c^3 and find it contradicting the consecutive integer a<b<c?)

I would go on with stating: b = a+1 ; c = b+1 <=> c = (a+1)+1

From here I am somewhat stuck.

Thank you!