The Singular Connection Between a Family of Exponential Functions and the Fermat-Wiles’ Theorem

The advances related to Modular Elliptic Curves and Femat's Last Theorem in recent years has opened the door to entirely new approaches to numerous problems and techniques. This paper studies the linking between a family of exponential function and the Fermat – Wiles’ theorem. In this family, the convergence of the coordinates of the maxima and the equation determined by the fulfilment of the maximum condition leads to a singular connection with the Fermat – Wiles’ theorem.