Rangan's Theory of Cycles

Age 14 to 18
Abhay sent us this investigation and discovery of some structural arithmetical patterns held by cyclic sets of natural numbers.

You can  read about his theory of cycles here.

Can you follow Abhay's argument? Does this fit into a larger structure about which you already know?  Perhaps you can suggest some generalisations?  

This article was authored by V. Abhay Rangan studying in 10th standard, in Poorna Prajna Education Centre, Indiranagar, Bangalore, India.