Journal article Open Access

Fermat Last Theorem and associated transformations of geometrical forms in number theory applications

Yuri K. Shestopaloff

Certain geometrical concepts associated with problems of number theory are presented. The approach is based on inherent relationship of properties of numbers, equations and their terms with corresponding geometrical forms. The notion of wrapping layers (wrapping geometrical forms around each other) was introduced. It was illustrated considering squares and parallelograms. Then, the concept of transformation of geometrical forms into other geometrical constructs was extended to n-dimensional space and applied to equation x^n + y^n = z^n. This equation has no solutions in natural numbers for n > 2. The result, formulated as Fermat Last Theorem (FLT), was proved by A. Wiles in 1995. Here, a simpler approach to the study of this problem is considered. The proposed concepts (a) are more consistent with a classic number theory; (b) equip the discipline with new methods and general ideas.

The paper presents the updated version of the material, deposited on public preprint servers, and also published in the following books: Shestopaloff Yu. K. (2018) Elementary Functions and Equations. Modeling Natural Phenomena. 2d Revised edition, AKVY Press, Toronto. Shestopaloff Yu. K. (2019) Elementary Functions and Equations. Fermat Last Theorem and Transformation of Geometrical Forms. 3d Revised edition, AKVY Press, Toronto.
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