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2019 CSMO Grade 10 Problem 4

Source: 2019 CSMO Grade 10 Problem 4

August 10, 2020
number theorymaximum valuecombinatorics proposed

Problem Statement

Let a1,a2,…,a17a_1,a_2,\dots, a_{17} be a permutation of 1,2,…,171,2,\dots, 17 such that (a1−a2)(a2−a3)…(a17−a1)=n17(a_1-a_2)(a_2-a_3)\dots(a_{17}-a_1)=n^{17} .Find the maximum possible value of nn .
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