Gauss's Problem
The Exact Solution of Gauss’s Problem on the Number
of Integer "Points" in a Circular and Spherical "Layers"
Arsen A. Movsesyan, engineer-physicist,
independent researcher, Этот адрес электронной почты защищен от спам-ботов. У вас должен быть включен JavaScript для просмотра.
Abstract. In the article, the Gauss’s problem on the number of integer points for a circle and a ball in the framework of an
integer lattice is reformulated in an equivalent way and reduces to solving two combinatorial tasks for a circular and spherical
"layer" in the framework of Quantum Discrete Space. These tasks are solved using trigonometric functions defined on a set of
integers whose range of values is also integers, and other new mathematical tools. It comes not about evaluative solutions, but
about exact solutions, which, if necessary, can be transferred to a circle and a ball. In doing so not only specific formulas for
determine the exact number of solutions are presented, but also the formulas for enumerating the corresponding pairs and triples
of integers. The importance of obtained solutions lies in the fact that they determine the analytical likenesses of not only the
circumference and the sphere in the Quantum Discrete Space, but also point to the possibility of constructing of the likenesses
of ellipse, cone, hyperboloid and other figures.
Keywords: Quantum Discrete Space; Gauss's Problem; Circular Passage; Spherical Passage
The full text of the article can be viewed here.