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 only case of consecutive perfect powers is 8 and 9.  This is Catalan's conjecture, which was proven to be true.
