There is no odd perfect polynomial over \(\mathbb F_{2}\) with four prime factors

DOI10.4171/PM/1836zbMath1193.11116OpenAlexW2065672914MaRDI QIDQ1018206

Luis H. Gallardo, Olivier Rahavandrainy

Publication date: 19 May 2009

Published in: Portugaliae Mathematica. Nova Série (Search for Journal in Brave)

Full work available at URL: http://www.ems-ph.org/journals/show_pdf.php?issn=0032-5155&vol=66&iss=2&rank=1

zbMATH Keywords

sum of divisorscharacteristic 2polynomials over finite fieldsperfect polynomials

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Arithmetic theory of polynomial rings over finite fields (11T55)

Related Items (13)

Unnamed Item ⋮ Some families of unitary perfect polynomials over \(\mathbb{F}_2\) ⋮ Counting perfect polynomials ⋮ All unitary perfect polynomials over \(\mathbb F_2\) with at most four distinct irreducible factors ⋮ On perfect polynomials over \(\mathbb{F}_p\) with \(p\) irreducible factors ⋮ On the index of special perfect polynomials ⋮ Unitary perfect polynomials over \(\mathbb {F}_4\) with less than five prime factors ⋮ Characterization of sporadic perfect polynomials over \(\mathbb{F}_2\) ⋮ On even (unitary) perfect polynomials over \(\mathbb F_2\) ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On Mersenne polynomials over \(\mathbb{F}_2\) ⋮ Fixed points of the sum of divisors function on \({{\mathbb{F}}}_2[x\)]

Cites Work

• Unnamed Item
• On perfect polynomials over \(\mathbb F_4\)
• Perfect polynomials over \(\mathbb F_4\) with less than five prime factors
• Odd perfect polynomials over \(\mathbb F_2\)
• The sum of the divisors of a polynomial
• Unsolved problems in number theory

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