Archive of Scientific Articles

Abstract. This paper proposes a method of Fermat’s theorem proof using the expansion of the original equation in series, which is of the form of a weighted additive function that depends on a single argument and parameters. The dependence of the function roots on the choice of weights is studied and the impossibility of the rational choice of weights is shown. Theoretical study is accompanied by calculations explaining the course of proving.

Key words and phrases: теория чисел, теорема Ферма, разложение уравнения в ряд, весовые коэффициенты, действительные корни функции, задача о наименьшем уклонении, theory of numbers, Fermat’s theorem, expansion of equation in series, weighted coefficients, real roots of function, problem on least deviation