On a problem in the theory of polynomials
-
Adrian Łydka
Abstract
In the paper, we solve a problem proposed by Schinzel and Bednarek: A monic polynomial f(x)2– 1 with deg(f) ≥ 3 is not a product of factors of degree one.
(Communicated by István Gaál)
References
[1] http://ntc.osu.cz/offline/sites/default/files/2013/NTC2013-Open_Problems.pdfSearch in Google Scholar
[2] Mignotte, M.—Stefanescu, D.: Polynomials. An Algorithmic Approach. Springer Series in Discrete Mathematics and Theoretical Computer Science, Springer-Verlag Singapore, Singapore; Centre for Discrete Mathematics and Theoretical Computer Science, Auckland, 1999.Search in Google Scholar
[3] Pólya, G.—Szegő, G.: Problems and Theorems in Analysis II. Theory of Functions, Zeros, Polynomials, Determinants, Number Theory, Geometry Springer-Verlag, Berlin, 1998.10.1007/978-3-642-61905-2Search in Google Scholar
© 2021 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular Papers
- Quasi-decompositions and quasidirect products of Hilbert algebras
- Residuation in finite posets
- On a problem in the theory of polynomials
- Fekete-Szegö problem for starlike functions connected with k-Fibonacci numbers
- Mapping properties of the Bergman projections on elementary Reinhardt domains
- Lemniscate-like constants and infinite series
- On the Oscillation of second order nonlinear neutral delay differential equations
- Oscillation theorems for certain second-order nonlinear retarded difference equations
- De la Vallée Poussin inequality for impulsive differential equations
- Hs-Boundedness of a class of Fourier Integral Operators
- Dynamical behavior of a P-dimensional system of nonlinear difference equations
- Some inequalities for exponentially convex functions on time scales
- Impact of different types of non linearity on the oscillatory behavior of higher order neutral difference equations
- The sine extended odd Fréchet-G family of distribution with applications to complete and censored data
- A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations
- Simulations of nonlinear parabolic PDEs with forcing function without linearization
- An existence level for the residual sum of squares of the power-law regression with an unknown location parameter
- A relationship between the category of chain MV-algebras and a subcategory of abelian groups
Articles in the same Issue
- Regular Papers
- Quasi-decompositions and quasidirect products of Hilbert algebras
- Residuation in finite posets
- On a problem in the theory of polynomials
- Fekete-Szegö problem for starlike functions connected with k-Fibonacci numbers
- Mapping properties of the Bergman projections on elementary Reinhardt domains
- Lemniscate-like constants and infinite series
- On the Oscillation of second order nonlinear neutral delay differential equations
- Oscillation theorems for certain second-order nonlinear retarded difference equations
- De la Vallée Poussin inequality for impulsive differential equations
- Hs-Boundedness of a class of Fourier Integral Operators
- Dynamical behavior of a P-dimensional system of nonlinear difference equations
- Some inequalities for exponentially convex functions on time scales
- Impact of different types of non linearity on the oscillatory behavior of higher order neutral difference equations
- The sine extended odd Fréchet-G family of distribution with applications to complete and censored data
- A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations
- Simulations of nonlinear parabolic PDEs with forcing function without linearization
- An existence level for the residual sum of squares of the power-law regression with an unknown location parameter
- A relationship between the category of chain MV-algebras and a subcategory of abelian groups
