Related papers: Congruent numbers on the right trapezoid

In the paper, we generalize some congruences of Lehmer for general composite numbers.

The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…

We consider right prisms with horizontal quadrilateral bases and tops, and vertical rectangular sides. We look for examples where all the edges, face diagonals and space diagonals are integers. We find examples when the base is an isosceles…

We settle the existence of certain "anti-magic" cubes using combinatorial block designs and graph decompositions to align a handful of small examples.

A new kind of numbers called Hyper Space Complex Numbers and its algebras are defined and proved. It is with good properties as the classic Complex Numbers, such as expressed in coordinates, triangular and exponent forms and following the…

In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed…

We continue our recent work on averages for ternary additive problems with powers of prime numbers.

A New Trinomial Recombination Tree Algorithm and Its Applications

We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) and/or diameter (maximum side-length), up to congruence. As we will see, this problem is considerably more difficult than the corresponding…

We mainly show a supercongruence for a truncated series with cubes of Catalan numbers which extends a result by Zhi-Wei Sun.

We introduce the three-Catalan triangle, highlighting the three-Catalan numbers along with their recurrence relation and combinatorial interpretation, which allows us to establish their log-convexity. Additionally, we prove that the rows of…

We present some interesting observations on the 3x+1 problem. We propose a new algorithm which eliminates certain steps while we check the action of 3x+1 procedure on a number. Also, we propose a reason why many numbers follow a similar…

We show various supercongruences for truncated series which involve central binomial coefficients and harmonic numbers. The corresponding infinite series are also evaluated.

We extend the use of piecewise orthogonal collocation to computing periodic solutions of renewal equations, which are particularly important in modeling population dynamics. We prove convergence through a rigorous error analysis. Finally,…

We study and give examples of braided groupoids, and, a fortiori, non-degenerate solutions of the quiver-theoretical braid equation.

In this article we prove some theorems related to the triplets of triangles, homological two by two. These theorems will be used later to build triplets of triangles two by two tri-homological.

The Jacobian algebras are introduced and their various properties are studied.

We propose a new approach to solve an NP complete problem by means of stochastic limit.

In this paper, we obtain the counting formulaes of convex pentagons and convex hexagons, respectively, in an $n$-triangular net by solving the corresponding recursive formulaes.

We reformulate the $3x+1$ conjecture by restricting attention to numbers congruent to $2$ (mod $3$). This leads to an equivalent conjecture for positive integers that reveals new aspects of the dynamics of the $3x+1$ problem. Advantages…