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The roots are the coefficients

Source: French TST 2012

August 2, 2012
algebrapolynomialalgebra unsolved

Problem Statement

Determine all non-constant polynomials Xn+an−1Xn−1+⋯+a1X+a0X^n+a_{n-1}X^{n-1}+\cdots +a_1X+a_0 with integer coefficients for which the roots are exactly the numbers a0,a1,…,an−1a_0,a_1,\ldots ,a_{n-1} (with multiplicity).
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