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Split numbers from 1 to 2n into two groups

Source: Mexico National Olympiad Mock Exam 2019 P4

October 16, 2019
number theoryDivisibility

Problem Statement

Find all positive integers nn such that it is possible to split the numbers from 11 to 2n2n in two groups (a1,a2,..,an)(a_1,a_2,..,a_n), (b1,b2,...,bn)(b_1,b_2,...,b_n) in such a way that 2n∣a1a2⋯an+b1b2⋯bn−12n\mid a_1a_2\cdots a_n+b_1b_2\cdots b_n-1.
Proposed by Alef Pineda
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