MathDB
Fantastic polynomial problem

Source: Kyiv City MO 2024 Round 1, Problem 10.4

January 28, 2024
algebrapolynomialnumber theory

Problem Statement

For a positive integer nn, does there exist a permutation of all its positive integer divisors (d1,d2,…,dk)(d_1 , d_2 , \ldots, d_k) such that the equation dkxk−1+…+d2x+d1=0d_kx^{k-1} + \ldots + d_2x + d_1 = 0 has a rational root, if:
a) n=2024n = 2024; b) n=2025n = 2025?
Proposed by Mykyta Kharin
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