Applied Physics and Mathematics Annotation << Back DETERMINATION OF THE ASYMPTOTIC BEHAVIOR OF THE NUMBER OF NATURAL SOLUTIONS OF CERTAIN TYPES OF DIAGONAL DIOPHANTINE EQUATIONS V.L. VOLFSON Diophantine equations are used to study complex discrete systems. Usually when searching for their optimal structures. Determining the number of natural solutions of Diophantine equations is used in economics. For example, when determining the number of options for drawing up a plan, etc. In this paper, we obtain asymptotic upper bounds for the number of natural solutions of the following diagonal Diophantine equations in a hypercube with side – N. Keywords: number of representations of a natural number, Hardy-Littlewood circular method, Hua lemma, Diophantine equation, Fermat equation, Thue equation, diagonal equation, number of natural solutions of the equation, asymptotic upper bound, hypercube with side, parametric solutions of the equation. DOI: 10.25791/pfim.06.2019.1045 Contacts: - Pp. 32-40.