| Abstrakt: |
We give a lower bound of the degree and the number of distinct prime divisors of the index of special perfect polynomials. More precisely, we prove that ω(d) ≥ 9, and deg(d) ≥ 258, where d := gcd(Q2 , σ(Q² )) is the index of the special perfect polynomial A := p²1Q², in which p1 is irreducible and has minimal degree. This means that σ(A) = A in the polynomial ring F2[x]. The function σ is a natural analogue of the usual sums of divisors function over the integers. The index considered is an analogue of the index of an odd perfect number, for which a lower bound of 135 is known. Our work use elementary properties of the polynomials as well as results of the paper. [ABSTRACT FROM AUTHOR] |
