Can consecutive integers be perfect powers? I have been  wondering whether consecutive integers can ever be perfect powers.And even if they can, how many consecutive integers at most can be perfect powers?My intuition tells me that consecutive integers can never be perfect powers,but I don't want to let that cloud my judgement.I haven't done any work,mainly because I don't know where to start.A hint that would help me start my proof will be appreciated.
EDIT: 8 and 9 clearly are perfect powers.I didn't know that it is called Catalan's conjecture.

The fact that there exist finitely many was first proved by Tidjeman and a complete proof that $8=2^3$ and $9=3^2$ is the only pair of consecutive powers was proved by Preda Mihăilescu in 2002 and published in 2004.
The proof is not an easy one to show here.
