On a Diophantine equation involving factorials.
On Cubic Polynomials III. Systems of p-adic Equations.
On Cubic Polynomials IV. Systems of Rational Equations.
On diagonal cubic surfaces.
On Heron triangles.
On nonary cubic forms: II.
On nonary cubic forms: III.
On -adic zeros of systems of diagonal forms restricted by a congruence condition
This paper is concerned with non-trivial solvability in -adic integers of systems of additive forms. Assuming that the congruence equation has a solution with we have proved that any system of additive forms of degree with at least variables, has always non-trivial -adic solutions, provided . The assumption of the solubility of the above congruence equation is guaranteed, for example, if .
On Pillai's Diophantine equation.
On polynomial-exponential equations.
On simultaneous additive equations II.
On simultaneous diagonal equations and inequalities
On some arithmetical properties of weighted sums of S-units.
On some equations over finite fields
In this paper, following L. Carlitz we consider some special equations of variables over the finite field of elements. We obtain explicit formulas for the number of solutions of these equations, under a certain restriction on and .
On systems of diophantine equations with a large number of solutions
We consider systems of equations of the form and , which have finitely many integer solutions, proposed by A. Tyszka. For such a system we construct a slightly larger one with much more solutions than the given one.
On the number of equivalence classes of binary forms of given degree and given discriminant
On the number of pairs of binary forms with given degree and given resultant
On the number of solutions of decomposable polynomial equations
On the representation of numbers by quaternary and quinary cubic forms: I
On the assumption of a Riemann hypothesis for certain Hasse-Weil L-functions, it is shewn that a quaternary cubic form f(x) with rational integral coefficients and non-vanishing discriminant represents through integral vectors x almost all integers N having the (necessary) property that the equation f(x)=N is soluble in every p-adic field ℚₚ. The corresponding proposition for quinary forms is established unconditionally.
On the resolution of index form equations in dihedral quartic number fields.