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Smallest integer

Source: Malaysia National Olympiad 2010 Sulung Category Problem 6

June 4, 2011
Diophantine equationalgebra unsolvedalgebra

Problem Statement

Find the smallest integer k≥3k\ge3 with the property that it is possible to choose two of the number 1,2,...,k1,2,...,k in such a way that their product is equal to the sum of the remaining k−2k-2 numbers.
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