Unfortunately, both of the proofs given in this thread appear to be faulty.

In the original proof (given by Captain Black), there is a missing minus sign, which prevents the proof from working.

And in my attempted proof for the correct version of the problem (with floor functions rather than ceilings), there is a missing

which also foils the proof.

So, if anyone would like to try and solve the problem, its still open...

Given:

Where k is a positive integer and

is the Omega constant, prove that

Any help, or ideally a really cool proof would be much appreciated.

Thanks

Rob