**Mileski Law** (or **Mileski
Theorem**) is first introduced in 2006 by
Robert Mileski, born in
Struga,
Republic of Macedonia. The law is defined for the complete
set of
integers.

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:

- where , and

the theorem
states that:

For a
monotonically increasing
integer sequence defined as:

- where , and

the
equality in the
equation
is achieved:

1. For the set of positive integers

- Example:

2. For monotonically increasing integer sequence defined as ,

- Example:

3. For the set of negative integers

- Example:

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**