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f(x^{n}) is divisible by x-1

Source: Polish MO Recond Round 1988 p1

September 9, 2024
algebrapolynomial

Problem Statement

Let f(x) f(x) be a polynomial, n n - a natural number. Prove that if f(xn) f(x^{n}) is divisible by x−1 x-1 , then it is also divisible by xn−1+xn−2+…+x+ x^{n-1} + x^{n-2} + \ldots + x + 1.
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