Problem

Source: 2019 CSMO Grade 10 Problem 4

Tags: number theory, maximum value, combinatorics proposed



Let $a_1,a_2,\dots, a_{17}$ be a permutation of $1,2,\dots, 17$ such that $(a_1-a_2)(a_2-a_3)\dots(a_{17}-a_1)=n^{17}$ .Find the maximum possible value of $n$ .