9790 /www/nrich/html/content/id/9790/ 5 2013-01-16T13:00:10 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Abhay sent us this investigation and discovery of some structural arithmetical patterns held by cyclic sets of natural numbers.<br></br> <br></br> You can  <a href="/content/id/9790/Theory%20of%20Cycles.pdf">read about his theory of cycles here</a>.<br></br> <br></br> Can you follow Abhay&#39;s argument? Does this fit into a larger structure about which you already know?  Perhaps you can suggest some generalisations?  <br></br> <br></br> If you wish to comment on the investigation or discuss it with others, you can use <a href="http://nrich.maths.org/discus/messages/27/154555.html">this thread</a> on the Ask NRICH forum<br></br> <br></br> <div class="framework">This article was authored by V. Abhay Rangan studying in 10th standard, in Poorna Prajna Education Centre, Indiranagar, Bangalore, India.</div> <br></br> <br></br></mdoxml> 2 0 0 0 0 1 1 In this beautifully written-up investigation Abhay describes his discovery of a 'theory of cycles'. sfh10 InvestigationBank