MathDB

9

Part of 2004 Baltic Way

Problems(1)

set of natural numbers

Source: Baltic Way 2004, problem 9

11/20/2004
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.
pigeonhole principlenumber theory unsolvednumber theory