Hemar Godinho

Generalized derivations and additive theory II

In this paper we investigate cyclic spaces of generalized derivations related to the symmetric functions, and its relation with a generalization of the Cauchy–Davenport Theorem.

On the Diophantine equation x2 + C= yn for C = 2a3b17c and C = 2a13b17c

Abstract In this paper, we find all solutions of the Diophantine equation x2 + C= yn in integers x, y ≥ 1, a, b, c ≥ 0, n ≥ 3, with gcd(x, y) = 1, when C= 2a3b17c and C = 2a13b17c.

Conditions for the solvability of systems of two and three additive forms over p -adic fields

This paper is concerned with non-trivial solvability in

Critical polynomials related to generalized derivations

p

A pair of additive quartic forms.

-adic integers of systems of two and three additive forms. Assuming that the congruence equation

Simultaneous diagonal equations over -adic fields

a x^k + b y^k + c z^k \equiv d \,(\mbox{mod}\,p)

On the diophantine equation v(v+1)=u(u+a)(u+2a)

has a solution with

Pairs of additive sextic forms

xyz \not\equiv 0\,(\mbox{mod}\,p)

On the Diophantine equation

we have proved that any system of two additive forms of odd degree

x^2+2^\alpha 5^\beta 17^\gamma =y^n

k