Problem #PRU-116873

Problems Methods Extremal principle Extremal principle (other) Mathematical induction Mathematical induction (other) Algebraic methods Partitions into pairs and groups; bijections Pigeonhole principle Pigeonhole principle (other)

14–15 4.0

Problem

We are given $n + 1$ different natural numbers, which are less than $2 n$ ( $n > 1$ ). Prove that among them there will always be three numbers, where the sum of two of them is equal to the third.

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