Remarks on a question of Skolem about the integer solutions of x₁x₂ - x₃x₄ = 1
Remarks on existentially closed fields and diophantine equations
Remarks on some new applications of the dispersion method
Remarks on the number of non-zero coefficients of polynomials.
Repdigits in the base as sums of four balancing numbers
The sequence of balancing numbers is defined by the recurrence relation for with initial conditions and is called the th balancing number. In this paper, we find all repdigits in the base which are sums of four balancing numbers. As a result of our theorem,...
Representability by certain norm forms over algebraic number fields
Représentation graphique de la résolution en nombres entiers de l’équation indéterminée
Representation of a prime as the sum of squares in a tower of fields.
Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids.
Representations of discriminantal divisors by binary quadratic forms.
Representations of every integer as the difference of nonsquare powerful numbers
Representations of integers by binary forms and the rank of the Mordell-Weil group.
Representations of multivariate polynomials by sums of univariate polynomials in linear forms
The paper is concentrated on two issues: presentation of a multivariate polynomial over a field K, not necessarily algebraically closed, as a sum of univariate polynomials in linear forms defined over K, and presentation of a form, in particular a zero form, as the sum of powers of linear forms projectively distinct defined over an algebraically closed field. An upper bound on the number of summands in presentations of all (not only generic) polynomials and forms of a given number of variables and...
Representing integers as linear combinations of S-units
Řešení diofantických rovnic rozkladem nad číselnými tělesy
Článek představuje zjednodušené základy teorie kvadratických zbytků a algebraické teorie čísel a jejich užití při řešení diofantických rovnic. Obsahuje i několik příkladů pro čtenáře.
Řešení rovnic neurčitých o více než dvou neznámých použitím řetězců
Řešení rovnice celými čísly
Rešenje diofantske jednačine
Résidus de puissances
Résolution de l’équation indéterminée en nombres entiers.