The introduction and the examination of the term “derivative” is a revolutionary moment in the history of mathematics. Due to this reason we pose the question: Which is the respective interpretation of this term in Number Theory ? This monograph answers that question. It also contains basic ideas from Theory of Differential Equations. In the first place, this is the Lagrange''s Method. Integer interpretations of basic theorems from Real Analysis have been examined. After all this, we have the opportunity to offer a proof of “Fermat''s Last Theorem” and some immediate generalizations. The author is married and has three children.