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System of equations: a√b - c = a; b√c - a = b; c√a - b = c

Source: Czech-Polish-Slovak Match, 2010

August 8, 2011
pigeonhole principlealgebrasystem of equationsalgebra unsolved

Problem Statement

Find all triples (a,b,c)(a,b,c) of positive real numbers satisfying the system of equations ab−c&=a,bc−a&=b,ca−b&=c. a\sqrt{b}-c \&= a,\qquad b\sqrt{c}-a \&= b,\qquad c\sqrt{a}-b \&= c.
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