Abstract. The paper studies the correlation of natural numbers set properties and Fermat’s theorem. The theorem proving, based on the above mentioned properties and the analysis of the limitations of supposed solutions, is proposed. The role of the acceptable transformations of variables included in the equation is studied, as well as the contributions of separate constituents depending on the values of characteristic quantities. Calculations confirm the correctness of the proving process.
Key words and phrases: теория чисел, натуральные числа, последняя теорема Ферма, ограничения на предполагаемые решения, допустимые преобразования, theory of numbers, natural numbers, Fermat’s last theorem, limitations of supposed solutions, acceptable transformations