Squarefree polynomials with prescribed coefficients

2017/07/20 by Oppenheim, Amotz, Shusterman, Mark · 1 citation
#05E99 #11N25 #11R29 #13P15 #14H05 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1707.06528

Abstract

For nonempty subsets S₀, …, S_n-1 of a (large enough) finite field \mathbbF satisfying |S₁|, …, |S_n-1| gt; 2 or |S₁|,|S_n-1| gt; n - 1, we show that there exist a₀ ∈ S₀, …, a_n-1 ∈ S_n-1 such that Tⁿ + a_n-1T^n-1 + … + a₁T + a₀ ∈ \mathbbF[T] is a squarefree polynomial.

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