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A class of irreducible polynomials

100%

Harrington J., Jones L.

Colloquium Mathematicum

2013

tom 132

nr 1

113-119

Let $f(x) = xⁿ + k_{n-1}x^{n-1} + k_{n-2}x^{n-2} + ⋯ +k₁x + k₀ ∈ ℤ[x]$, where $3 ≤ k_{n-1} ≤ k_{n-2} ≤ ⋯ ≤ k₁ ≤ k₀ ≤ 2k_{n-1} - 3$. We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of $2k_{n-1} - 3$ on the coefficients of f(x) is the best possible in this situation.

A polynomial investigation inspired by work of Schinzel and Sierpiński

100%

Filaseta M., Harrington J.

Acta Arithmetica

2012

tom 155

nr 2

149-161

Ograniczanie wyników

1 Acta Arithmetica

1 Colloquium Mathematicum

2 Harrington J.

1 Filaseta M.

1 Jones L.

1 2013

1 2012

Wyniki wyszukiwania

A class of irreducible polynomials

A polynomial investigation inspired by work of Schinzel and Sierpiński