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Irregularities in the distribution of irreducible polynomials


Author: Kevin S. McCurley
Journal: Proc. Amer. Math. Soc. 117 (1993), 11-16
MSC: Primary 11T06
DOI: https://doi.org/10.1090/S0002-9939-1993-1107923-5
MathSciNet review: 1107923
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Abstract: We prove that there exist monic polynomials $ f$ over $ \operatorname{GF} (q)$ for which $ f + g$ is reducible for all $ g \in \operatorname{GF} (q)[x]$ with small degree. This is the analogue for polynomials of a result of Erdös and Rankin concerning gaps between consecutive primes.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1107923-5
Article copyright: © Copyright 1993 American Mathematical Society