The FFT - multiple binary splitting

The FFT is essentially a multipass version of binary splitting.

If is the number of multiplications needed to compute the DFT with N data points, ,  then the following recursive equation reflects the fact that you can use binary splitting to replace an N point DFT with two point DFT's and then once you get these two results you need to do additional multiplications.
        
        and  
        
The solution to this recurrence relation is  .