论文标题
所有甚至（统一的）完美多项式超过$ \ f_2 $，只有梅森·普里姆（Mersenne Primes）
All even (unitary) perfect polynomials over $\F_2$ with only Mersenne primes as odd divisors
论文作者
论文摘要
我们在环$ \ f_2 [x] $中解决与除数总和的固定点有关的算术问题。我们研究一些二进制多项式$ a $，因此$σ（a）/a $仍然是二进制多项式。从技术上讲，我们证明，$ \ f_2 $的唯一（统一）完美的多项式是$ x $，$ x+1 $的产品，而Mersenne Primes的产品恰恰是九个已知的（分别是九个“类”）。这是从$ m^{2H +1} +1 $的分解的新结果中，对于Mersenne Prime $ M $和正整数$ h $。
We address an arithmetic problem in the ring $\F_2[x]$ related to the fixed points of the sum of divisors function. We study some binary polynomials $A$ such that $σ(A)/A $ is still a binary polynomial. Technically, we prove that the only (unitary) perfect polynomials over $\F_2$ that are products of $x$, $x+1$ and of Mersenne primes are precisely the nine (resp. nine "classes") known ones. This follows from a new result about the factorization of $M^{2h+1} +1$, for a Mersenne prime $M$ and for a positive integer $h$.
