Proof of Fermat Last Theorem based on successive presentations of pairs of odd numbers

A simpler proof of Fermat Last Theorem (FLT), formulated by Fermat in 1637, is suggested. The initial equation x^n + y^n = z^n is considered not in natural, but in integer numbers. It is subdivided into four equations based on parity of terms and their powers. All cases converge to one equation, which is studied using presentation of pairs of odd integers with a successively increasing presentation factor of 2^r. At each presentation level, the equation has no solution for a certain subset of pairs of odd integers. Using introduced measure of such "no solution" subsets, we sum up the corresponding measures across subsequent presentation levels, and prove that this sum corresponds to all possible pairs of odd integers. Based on this result, we eventually prove that FLT equation has no integer solution. The proposed methods and ideas can be used for studying other problems in number theory.