The Danielson-Lancoz lemma shows that a sequence must be divided up into its odd and even subsets. That these subsets must in-turn be divided into their subsets. This continues until we have only two members per subset.
Journal of Object Technology
Lyon, Douglas A., "The Discrete Fourier Transform, Part 2: Radix 2 FFT" (2009). Engineering Faculty Publications. 75.
Douglas Lyon, “The Discrete Fourier Transform, Part 2: Radix 2 FFT”, Journal of Object Technology, Volume 8, no. 5 (July 2009), pp. 21-33