On the largest irreducible factor of an odd perfect polynomial over $\mathbb{F}_2$
Source: hexagonmath.org/abs/2611.00030v1
A polynomial $A$ over $\mathbb{F}_2$ is perfect if it equals the sum $\sigma(A)$ of all its divisors, and odd if it is coprime to $x^2+x$. Canaday conjectured in 1941 that 1 is the only odd perfect polynomial. Known necessary conditions on a counterexample bound its number of distinct irreducible factors ($\omega\ge 5$, Gallardo and Rahavandrainy), its number of irreducible factors counted with multiplicity and its degree ($\Omega\ge 12$ and $\deg A>200$, Cengiz, Pollack and Trevino), and, when all exponents equal 2, the degree of its smallest irreducible factor (at least 40, Gallardo). We…
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