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No subsets divisible with n+1

Source: Romanian TST 1 2008, Problem 1

May 1, 2008
modular arithmeticnumber theoryrelatively primecombinatorics proposedcombinatorics

Problem Statement

Let n n be an integer, n≥2 n\geq 2. Find all sets A A with n n integer elements such that the sum of any nonempty subset of A A is not divisible by n\plus{}1.
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