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(c^2-a^2)/b+(b^2-c^2)/a=b-a , where a,b,c sidelengths of triangle

Source: Finland 2016, Problem 1

September 8, 2019
algebrageometrysidelengths

Problem Statement

Which triangles satisfy the equation c2−a2b+b2−c2a=b−a\frac{c^2-a^2}{b}+\frac{b^2-c^2}{a}=b-a when a,ba, b and cc are sides of a triangle?
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