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n roots of polynomial form an arithmetic sequence

Source: 2017 Saudi Arabia IMO Training Test p4

September 4, 2020
arithmetic sequencealgebrapolynomial

Problem Statement

Does there exist an integer n≥3n \ge 3 and an arithmetic sequence a0,a1,...,ana_0, a_1, ... , a_n such that the polynomial anxn+...+a1x+a0a_nx^n +... + a_1x + a_0 has nn roots which also form an arithmetic sequence?
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