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permutaion of 1,2,..., n with any 2 adjacent is 2015 or 2016

Source: 2016 Saudi Arabia Pre-TST Level 4+ 2.1

September 13, 2020
combinatoricspermutation

Problem Statement

1) Prove that there are infinitely many positive integers nn such that there exists a permutation of 1,2,3,...,n1, 2, 3, . . . , n with the property that the difference between any two adjacent numbers is equal to either 20152015 or 20162016. 2) Let kk be a positive integer. Is the statement in 1) still true if we replace the numbers 20152015 and 20162016 by kk and k+2016k + 2016, respectively?
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