I wanted to Cite this article below for the idea of the geometry
which I changed some and added my own idea's.
By: Kaida Shi - Fermat's Theorem
State Key Laboratory of CAD&CG, Zhejiang University,
Hangzhou 310027, Zhejiang Province, China
Abstract By researching the n-dimensional cube, the author found a new way, and
proved that the indefinite equation x n + y n = z n (n ≥ 3) has no any solutions of positive
integers.