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Let K be a field and P∈K[X] is a polynomial of degree n, then the conjecture of Casas-Alvero states that if P is not prime with each of its n−1 first derivatives, then it is a monomial, i.e., of the form c(X−r)n. We consider the case where K=ℝ and P is split over ℝ, where we show that the number un of hypothetical counterexamples of degree n satisfies (n−4)!≤un≤c(n−3)n−2, where c=2e−1(∏n=2∞e−1(∑k=0n1/k!))2=0...
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