2019/03/27 by Ivan D. Chipchakov, Chipchakov, Ivan D.
Mathematics · #Analytic Number Theory Research #Advanced Differential Equations and Dynamical Systems #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1903.11321
Let K be a field and f n(X) = (X + 1) n + (-1) n(X n + 1) ∈ K[X], for each n ∈ \mathbb N. This note shows that the polynomials f m(X) and f m'(X) are relatively prime, for some distinct indices m and m ′ at most equal to 100, if and only if the product mm ′ is divisible by 6.