Abstract
In this paper, we show that there is no polynomial D(n)-quadruple in ℤ[X] for some polynomials n ∈ ℤ[X] that are not representable as a difference of squares of two polynomials in ℤ[X].
This work was supported by the Croatian Science Foundation Grant No. IP-2022-10-5008. The first author Z.F. acknowledges support from the project “Implementation of cutting-edge research and its application as part of the Scientific Center of Excellence for Quantum and Complex Systems, and Representations of Lie Algebras”, PK.1.1.02, European Union, European Regional Development Fund
Communicated by István Gaál
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© 2024 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- 10.1515/ms-2024-frontmatter4
- Intervals of posets of a zero-divisor graph
- Coalgebraic methods for Ramsey degrees of unary algebras
- On nonexistence of D(n)-quadruples
- Rees short exact sequences and preenvelopes
- Generalized discrete Grüss and related results with applications
- Radius problem associated with certain ratios and linear combinations of analytic functions
- Existence results for a fourth order problem with functional perturbed clamped beam boundary conditions
- Oscillatory and asymptotic behavior of even-order nonlinear differential equations with mixed neutral terms
- On a solvable four-dimensional system of difference equations
- Euclidean operator radius inequalities of d-tuple operators and operator matrices
- Equable parallelograms on the Eisenstein lattice
- On certain star versions of the Hurewicz property using ideals
- Relative versions of star-Menger property
- The Maxwell-Boltzmann-Exponential distribution with regression model
- New results for the Marshall-Olkin family of distributions
- A new family of copulas based on probability generating functions
- Induced mappings on the hyperspace of totally disconnected sets
Artikel in diesem Heft
- 10.1515/ms-2024-frontmatter4
- Intervals of posets of a zero-divisor graph
- Coalgebraic methods for Ramsey degrees of unary algebras
- On nonexistence of D(n)-quadruples
- Rees short exact sequences and preenvelopes
- Generalized discrete Grüss and related results with applications
- Radius problem associated with certain ratios and linear combinations of analytic functions
- Existence results for a fourth order problem with functional perturbed clamped beam boundary conditions
- Oscillatory and asymptotic behavior of even-order nonlinear differential equations with mixed neutral terms
- On a solvable four-dimensional system of difference equations
- Euclidean operator radius inequalities of d-tuple operators and operator matrices
- Equable parallelograms on the Eisenstein lattice
- On certain star versions of the Hurewicz property using ideals
- Relative versions of star-Menger property
- The Maxwell-Boltzmann-Exponential distribution with regression model
- New results for the Marshall-Olkin family of distributions
- A new family of copulas based on probability generating functions
- Induced mappings on the hyperspace of totally disconnected sets