Even perfect polynomials over $F_2$ with four prime factors

Details Even perfect polynomials over $F_2$ with four prime factors Even perfect polynomials over $F_2$ with four prime factors

2007-12-16

arxiv.org/abs/0712.2602v1

Mathematics

Number Theory

19 pages (in 12 pt)

Scientific paper

A perfect polynomial over the binary field $\F_2$ is a polynomial $A \in \F_2[x]$ that equals the sum of all its divisors. If $\gcd(A,x^2-x) \neq 1$ then we call $A$ even. The list of all even perfect polynomials over $\F_2$ with at most 3 prime factors in known. The object of this paper is to give the list of all even perfect polynomials over $\F_2$ with four prime factors. These are all the known perfect polynomials with four prime factors over $\F_2$.

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