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2 number from 1-n such that their product = sum of other n-2

Source: 2008 Swedish Mathematical Competition p2

April 27, 2021
number theorycombinatorics

Problem Statement

Determine the smallest integer n≥3n \ge 3 with the property that you can choose two of the numbers 1,2,…,n1,2,\dots, n in such a way that their product is equal to the sum of the other n−2n - 2 languages. What are the two numbers?
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