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Let $f (x) = x ⁿ + k_{n - 1} x^{n - 1} + k_{n - 2} x^{n - 2} + \dots + k ₁ x + k ₀ \in ℤ [x]$ , where $3 \leq k_{n - 1} \leq k_{n - 2} \leq \dots \leq k ₁ \leq k ₀ \leq 2 k_{n - 1} - 3$ . We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of $2 k_{n - 1} - 3$ on the coefficients of f(x) is the best possible in this situation.

A Class of Periodic Jacobi-Perron Algorithms in Pure Algebraic Number Fields of Degree n...3.

Claude Levesque (1977)

Manuscripta mathematica

A class of permutation trinomials over finite fields

Xiang-dong Hou (2014)

Acta Arithmetica

Let q > 2 be a prime power and $f = - x + t x^{q} + x^{2 q - 1}$ , where $t \in *_{q}$ . We prove that f is a permutation polynomial of $_{q ²}$ if and only if one of the following occurs: (i) q is even and $T r_{q / 2} (1 / t) = 0$ ; (ii) q ≡ 1 (mod 8) and t² = -2.

A class of polynomials

Andrzej Schinzel (1991)

Mathematica Slovaca

A class of symmetric 2-bases.

Torleiv Klove (1980)

Mathematica Scandinavica

A class of symmetric biadditive functionals.

P. Fischer, J.P. Mokansi (1981)

Aequationes mathematicae

A class of transcendental numbers having explicit g-adic and Jacobi-Perron expansions of arbitrary dimension

Jun-Ichi Tamura (1995)

Acta Arithmetica

A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm

Jun-ichi Tamura (1992)

Acta Arithmetica

In this paper, we give transcendental numbers φ and ψ such that (i) both φ and ψ have explicit g-adic expansions, and simultaneously, (ii) the vector $^{t} (φ, ψ)$ has an explicit expression in the Jacobi-Perron algorithm (cf. Theorem 1). Our results can be regarded as a higher-dimensional version of some of the results in [1]-[5] (see also [6]-[8], [10], [11]). The numbers φ and ψ have some connection with algebraic numbers with minimal polynomials x³ - kx² - lx - 1 satisfying (1.1) k ≥ l ≥0, k + l ≥ 2 (k,l...

A class of weakly perfect graphs

H. R. Maimani, M. R. Pournaki, S. Yassemi (2010)

Czechoslovak Mathematical Journal

A graph is called weakly perfect if its chromatic number equals its clique number. In this note a new class of weakly perfect graphs is presented and an explicit formula for the chromatic number of such graphs is given.

A class–field theoretical calculation

Cristian D. Popescu (2006)

Journal de Théorie des Nombres de Bordeaux

In this paper, we give the complete characterization of the $p$ –torsion subgroups of certain idèle–class groups associated to characteristic $p$ function fields. As an application, we answer a question which arose in the context of Tan’s approach [6] to an important particular case of a generalization of a conjecture of Gross [4] on special values of $L$ –functions.

A Classical Diophantine Problem and Modular Forms of Weight 3/2.

J.B. Tunnell (1983)

Inventiones mathematicae

A classification of rank 6 quadratic spaces via pfaffians.

R. Sridharan, M.-A. Knus, R. Parimala (1989)

Journal für die reine und angewandte Mathematik

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