MathDB
n! good sets

Source: 239 2019 J5

July 31, 2020
combinatoricsinduction

Problem Statement

We call an ordered set of distinct natural numbers good if for any two numbers in it, the larger one is divided by the smaller one. Prove that the number (n+1)!–1(n + 1)! – 1 can be represented as x1+2x2+…+nxnx_1 + 2x_2 + \ldots + nx_n, where {x1,x2,…,xn}\{ x_1, x_2, \ldots , x_n \} is a good set, by at least n!n! ways.
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