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product of the 31 numbers is 5th power, from pairs of 0-61

Source: 2022 NZMO - New Zealand Maths Olympiad Round 1 p2

October 9, 2022
number theorypower of numberPerfect power

Problem Statement

Is it possible to pair up the numbers 0,1,2,3,...,610, 1, 2, 3,... , 61 in such a way that when we sum each pair, the product of the 3131 numbers we get is a perfect f ifth power?
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