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MathNet 2009-part-02 — 175 problems (EN–VI) Question 73

Math Olympiad Vault · MathNet 2009-part-02 — 175 problems (EN–VI)

Question 73

Francesco wants to write the polynomial $x^{16}+x$ as a product of several polynomials with integer coefficients, each of degree at least 1. What is the maximum number of factors he can obtain?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5 .