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Romanian District Olympiad 2009 - Grade 12 - Problem 4

Source: Romanian District Olympiad 2009 - Grade 12 - Problem 4

August 17, 2024
superior algebraPolynomialsfinite fieldprobability

Problem Statement

Let KK be a finite field with qq elements and let n≥qn \ge q be an integer. Find the probability that by choosing an nn-th degree polynomial with coefficients in K,K, it doesn't have any root in K.K.
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