Rational points on some elliptic surfaces
Rational points on some pencils of conics with 6 singular fibres
Rational products of sines of rational angles.
Rational solutions of certain Diophantine equations involving norms
We present some results concerning the unirationality of the algebraic variety given by the equation , where k is a number field, K=k(α), α is a root of an irreducible polynomial h(x) = x³ + ax + b ∈ k[x] and f ∈ k[t]. We are mainly interested in the case of pure cubic extensions, i.e. a = 0 and b ∈ k∖k³. We prove that if deg f = 4 and contains a k-rational point (x₀,y₀,z₀,t₀) with f(t₀)≠0, then is k-unirational. A similar result is proved for a broad family of quintic polynomials f satisfying...
Rational triangles with equal area.
Rationale Punkte auf Fermatkurven und getwisteten Modulkurven.
Rationale Tetraeder.
Rationals Not Expressible as a Sum of Three Unit Fractions.
Recipes for Solving Diophantine Problems by Baker's Method
Reciprocity in valued function fields.
Reduction of an arbitrary diophantine equation to one in 13 unknowns
Reflections on Fermat's Last Theorem.
Regular solutions of a congruence system.
Relations diophantiennes et la solution négative du 10e problème de Hilbert
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