Given a set of $1997$ numbers such that if each number in the set, replace with the sum of the rest, you get the same set. Prove that the product of numbers in the set is equal to $0$.
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Tags: combinatorics, number theory
Given a set of $1997$ numbers such that if each number in the set, replace with the sum of the rest, you get the same set. Prove that the product of numbers in the set is equal to $0$.