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Romania tst

Source: Romania TST for IMO 1994,third test

September 6, 2017
algebranumber theory

Problem Statement

Let pp be a (positive) prime number. Suppose that real numbers a1,a2,...,ap+1a_1, a_2, . . ., a_{p+1} have the property that, whenever one of the numbers is deleted, the remaining numbers can be partitioned into two classes with the same arithmetic mean. Show that these numbers must be equal.
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