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Real, rational, integers

Source: Indonesia Mathematics Olympiad 2006 Day 2 Problem 7

June 2, 2008
algebra proposedalgebra

Problem Statement

Let a,b,c a,b,c be real numbers such that ab,bc,ca ab,bc,ca are rational numbers. Prove that there are integers x,y,z x,y,z, not all of them are 0 0, such that ax\plus{}by\plus{}cz\equal{}0.
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