This rule applies to a monotonically increasing sequence of positive integers or monotonically decreasing sequence of negative integers, and states that the sum of two consecutive elements of the sequence is smaller or equal to the difference of their squares.
For a given sequence:
the theorem states that:
If you want to test the theorem how it works, I've developed a small web page, where you can run your sequences and test: http://mileskitheorem.brinkster.net/default.aspx
I would like to thank Aneta Koseska for supporting me in my work, as well as guiding me how to make this better.
If you have any questions or comments, please feel free to send me an email : r_mileski(at)yahoo.com