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the sum of p numbers is divisible by p

Source: Erdos-Ginzburg-Zif theorem

March 5, 2005
inequalitiesmodular arithmeticalgorithminductionnumber theorynumber theory unsolved

Problem Statement

We have 2p−12p-1 integer numbers, where pp is a prime number. Prove that we can choose exactly pp numbers (from these 2p−12p-1 numbers) so that their sum is divisible by pp.
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