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f(a,b,c) = (a+b+c, ab+bc+ca, abc)

Source: Indian National Maths Olympiad, Problem 3

February 5, 2006
analytic geometryalgebra proposedalgebra

Problem Statement

Let X=Z3X=\mathbb{Z}^3 denote the set of all triples (a,b,c)(a,b,c) of integers. Define f:Xā†’Xf: X \to X by f(a,b,c)=(a+b+c,ab+bc+ca,abc). f(a,b,c) = (a+b+c, ab+bc+ca, abc) . Find all triples (a,b,c)(a,b,c) such that f(f(a,b,c))=(a,b,c). f(f(a,b,c)) = (a,b,c) .
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