Waring's problem for polynomial cubes and squares over a finite field with odd characteristic.
On Rolle's theorem for polynomials over the complex numbers.
On Fail-Rolle polynomials with few roots.
On perfect polynomials over .
A class of discriminant varieties in the conformal 3-sphere.
On the restricted Waring problem over
1. Introduction. The Waring problem for polynomial cubes over a finite field F of characteristic 2 consists in finding the minimal integer m ≥ 0 such that every sum of cubes in F[t] is a sum of m cubes. It is known that for F distinct from ₂, ₄, , each polynomial in F[t] is a sum of three cubes of polynomials (see [3]). If a polynomial P ∈ F[t] is a sum of n cubes of polynomials in F[t] such that each cube A³ appearing in the decomposition has degree < deg(P)+3, we say that P is a restricted...
Sums of cubes of polynomials
Odd perfect polynomials over
A perfect polynomial over is a polynomial that equals the sum of all its divisors. If then we say that is odd. In this paper we show the non-existence of odd perfect polynomials with either three prime divisors or with at most nine prime divisors provided that all exponents are equal to
Solving quadratic equations over polynomial rings of characteristic two.
We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation antn + ...+ a0 = 0 with coefficients ai in A, our problem is to find its roots in A. We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction, we obtain...
On a binary recurrent sequence of polynomials
In this paper, we study the properties of the sequence of polynomials given by , for , where is non-constant and the characteristic of is . This complements some results from R. Euler, L.H. Gallardo: On explicit formulae and linear recurrent sequences, Acta Math. Univ. Comenianae, 80 (2011) 213-219.
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