The “Kronecker approach” is being developed to the study of general problems of number theory, in a very broad sense related to the theory of solutions of Diophantine equations. Such an “elementary” approach to some well-known facts of quadratic forms of a number can be transferred almost directly to the case of integral Euclidean rings (when we have division with remainder). In this formulation, well-known results are obtained quite simply (for example, Fermat-Euler’s Theorem), as well as some new facts concerning quadratic forms for representing prime numbers as such, as well as doubled or tripled ones in particular.

division with a remainder, alternative divisibility, quadratic form of number representation.

Received: March 26, 2021; Accepted: April 26, 2021; Published: July 3, 2021

How to cite this article: V. A. Danilov, A. V. Daneev and V. A. Rusanov, A new look at some facts of number theory: alternate divisibility when constructing simple solutions to problems of arithmetic, JP Journal of Algebra, Number Theory and Applications 51(2) (2021), 125-143. DOI: 10.17654/NT051020125

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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