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Paraguayan National Olympiad 2008, Level 3, Problem 5

Source:

August 31, 2014
symmetry

Problem Statement

Let m,n,pm,n,p be rational numbers such that m+n+p\sqrt{m} + \sqrt{n} + \sqrt{p} is a rational number. Prove that m,n,p\sqrt{m}, \sqrt{n}, \sqrt{p} are also rational numbers
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