Odd perfect polynomials over F2
نویسندگان
چکیده
A perfect polynomial over F2 is a polynomial A ∈ F2[x] that equals the sum of all its divisors. If gcd(A, x + x) = 1 then we say that A is odd. In this paper we show the non-existence of odd perfect polynomials with either three prime divisors or with at most nine prime divisors provided that all exponents are equal to 2.
منابع مشابه
Counting perfect polynomials
Let A ∈ F2[T ]. We say A is perfect if A coincides with the sum of all of its divisors in F2[T ]. We prove that the number of perfect polynomials A with |A| ≤ x is O (x1/12+ ) for all > 0, where |A| = 2degA. We also prove that every perfect polynomial A with 1 < |A| ≤ 1.6× 1060 is divisible by T or T + 1; that is, there are no small “odd” perfect polynomials.
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