MathDB

A2

Part of 2023 Romanian Master of Mathematics Shortlist

Problems(1)

Consecutive roots and interpolation

Source: RMM Shortlist 2023 A2

2/29/2024
Fix an integer n≥2n \geq 2 and let a1,…,ana_1, \ldots, a_n be integers, where a1=1a_1 = 1. Let f(x)=∑m=1nammx. f(x) = \sum_{m=1}^n a_mm^x. Suppose that f(x)=0f(x) = 0 for some KK consecutive positive integer values of xx. In terms of nn, determine the maximum possible value of KK.
interpolationalgebraPolynomialsRMM Shortlist