All of the numbers are equal - [Iran Second Round 1988]
Source:
December 7, 2010
logarithmsnumber theory proposednumber theory
Problem Statement
Let be a positive integer. positive rational numbers are given with this property: if we remove one of the numbers, then we can divide remain numbers into sets with equal number of elements such that the product of the numbers of the sets be equal. Prove that all of the numbers are equal.