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2017 Polish Junior Math Olympiad First Round P1

Source: 2017 Polish Junior Math Olympiad First Round

May 23, 2023
algebranumber theory

Problem Statement

Rational numbers aa, bb, cc satisfy the equation (a+b+c)(a+b−c)=c2 .(a+b+c)(a+b-c)=c^2\,. Show that a+b=c=0a+b=c=0.
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