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a,b,c in one of two disjoint sets such that ab=c

Source: BdMO 2022 Secondary P3

April 12, 2022
algebra

Problem Statement

Prove that if the numbers 3,4,5,…,353,4,5, \dots ,3^5 are partitioned into two disjoint sets, then in one of the sets the number a,b,ca,b,c can be found such that ab=c.ab=c. (a,b,ca,b,c may not be pairwise distinct)
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