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set of natural numbers

Source: Baltic Way 2004, problem 9

November 20, 2004
pigeonhole principlenumber theory unsolvednumber theory

Problem Statement

A set SS of n−1n-1 natural numbers is given (n≥3n\ge 3). There exist at least at least two elements in this set whose difference is not divisible by nn. Prove that it is possible to choose a non-empty subset of SS so that the sum of its elements is divisible by nn.
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