Abstract: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 $\omega(d) \geq 9$, and $\deg(d) \geq 258$, where $d := \gcd(Q^2,\sigma(Q^2))$ is the index of the special perfect polynomial $A := p_1^2 Q^2$, in which $p_1$ is irreducible and has minimal degree. This means that $ \sigma(A)=A$ in the polynomial ring ${\mathbb{F}}_2[x]$. The function $\sigma$ is a natural analogue of the usual sums of divisors function over t… Show more
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