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pable numbers

Source: Netherlands TST for IMO 2017 day 2 problem 3

February 1, 2018
number theory

Problem Statement

Let k>2k > 2 be an integer. A positive integer ll is said to be k−pablek-pable if the numbers 1,3,5,...,2k−11, 3, 5, . . . , 2k - 1 can be partitioned into two subsets AA and BB in such a way that the sum of the elements of AA is exactly ll times as large as the sum of the elements of BB. Show that the smallest k−pablek-pable integer is coprime to kk.
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