Related papers: An alternative quadratic formula
A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
In Lett. Math. Phys. 114, 54 (2024) and 115, 70 (2025), the author introduces what is presented as a novel method for determining whether a sequence of orthogonal polynomials is "classical", based solely on its initial recurrence…
Highly efficient and even nearly optimal algorithms have been developed for the classical problem of univariate polynomial root-finding (see, e.g., \cite{P95}, \cite{P02}, \cite{MNP13}, and the bibliography therein), but this is still an…
We look at the number of solutions of an equation of the form f_1*f_2*...*f_k=a in a finite field, where each f_i is a multilinear polynomial. We use two methods to construct a solution of this problem for the cases a=0, a<>0, and we…
Using the circle method, we obtain asymptotic formulae for the number of integer solutions to certain quadratic polynomials that are uniform in the coefficients of the polynomial.
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
We introduce an object that has obvious similarity to the classical one - the algebra of supersymmetric polynomials. Despite the similarity, the known structure theorems on supersymmetric polynomials do not help in the study of the new…
This note gives an elementary exposition of a variant of the spread polynomials in terms of Fibonacci and Lucas polynomials.
We prove that the alternative Clifford algebra of a nondegenerate ternary quadratic form is an octonion algebra over the ring of polynomials in one variable over the field of definition.
The central idea of this article is to present a systematic approach to construct some recurrence relations for the solutions of the second-order linear difference equation of hypergeometric-type defined on the quadratic-type lattices. We…
This note presents new results for the squarefree value sets of quartic polynomials over the integers.
We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.
We propose a new approach at Fermat's Last Theorem (FLT) solution: for each FLT equation we associate a polynomial of the same degree. The study of the roots of the polynomial allows us to investigate the FLT validity. This technique,…
We present some new linear, quadratic, cubic and quartic binomial Fibonacci, Lucas and Fibonacci--Lucas summation identities.
In the present study, we propose necessary and sufficient assumptions on the coefficients in order to only get distinct real roots of polynomials.
We give a formula for matrix exponentials and partial fraction decompositions.
We introduce and discuss a multivariate version of the classical median that is based on an equipartition property with respect to quarter spaces. These arise as pairwise intersections of the half-spaces associated with the coordinate…
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…