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Problems(1)

Partitioning {1, 2, ... ,49} in three subsets

Source:

10/11/2010
The set {1,2,⋯ ,49}\{1, 2, \cdots, 49\} is divided into three subsets. Prove that at least one of these subsets contains three different numbers a,b,ca, b, c such that a+b=ca + b = c.
inequalitiesnumber theory unsolvednumber theory