All unitary perfect polynomials over F2 with at most four distinct irreducible factors

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Abstract

A polynomial AF2[x] is unitary perfect if and only if A=dA,gcd(d,A/d)=1d. We find all unitary perfect polynomials of the form P1a1P2a2P3a3P4a4 where P1,,P4F2[x] are irreducible polynomials and a1,,a4 are non-negative integers.

Keywords

Sum of divisors
Unitary divisors
Polynomials
Finite fields
Characteristic 2

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