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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Distinct degree factorizations for polynomials over a finite field

Authors: Arnold Knopfmacher and Richard Warlimont
Journal: Trans. Amer. Math. Soc. 347 (1995), 2235-2243
MSC: Primary 11T06; Secondary 11T55
MathSciNet review: 1277121
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Abstract: Let $ {\widetilde{\mathbb{F}}_q}[X]$ denote the multiplicative semigroup of monic polynomials in one indeterminate $ X$, over a finite field $ {\mathbb{F}_q}$. We determine for each fixed $ q$ and fixed $ n$ the probability that a polynomial of degree $ n$ in $ {\mathbb{F}_q}[X]$ has irreducible factors of distinct degrees only. These results are of relevance to various polynomial factorization algorithms.

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