MathDB
Sequence as Coefficients

Source: 2024 Taiwan TST Round 3 Mock P6

April 27, 2024
TaiwanpolynomialSequencealgebra

Problem Statement

Find all positive integers nn and sequence of integers a0,a1,…,ana_0,a_1,\ldots, a_n such that the following hold: 1. an≠0a_n\neq 0; 2. f(ai−1)=aif(a_{i-1})=a_i for all i=1,…,ni=1,\ldots, n, where f(x)=anxn+an−1xn−1+⋯+a0f(x) = a_nx^n+a_{n-1}x^{n-1}+\cdots +a_0.
Proposed by usjl
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