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divide divisors into two groups with equal product if their product is a perfect

Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 1 E4

November 29, 2022
number theoryPerfect SquaresDivisors

Problem Statement

Show that the divisors of a number n2n \ge 2 can only be divided into two groups in which the product of the numbers is the same if the product of the divisors of nn is a square number.