Odd number - factor theorem with proof Abstract: This theorem is based on the basic structure from the odd-cut, according to odd-numbered - factor - the variance between them relations of mutual dependence, into a number of objective reality and between the general law. As well as Pythagoras theorem and Fermat's last theorem summarizes the total. Key words: prove that odd, factors, variance theorem. Introduction: This is the field of mathematics based on a major discovery, simply put, is an extension of the theory of Pythagorean Theorem. So far, no one textbook, has not been documented, it is extremely simple and easy to prove that people are often overlooked issue. Filled the multiplication formula for the involution on the decomposition of a number of gaps, and its role may not be taken lightly.