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f(\pi) is a square, f : \pi \to \pi, image of any triangle is a square

Source: Romania IMO TST 1992 p3

February 19, 2020
functionTrianglealgebra

Problem Statement

Let π\pi be the set of points in a plane and f:π→πf : \pi \to \pi be a mapping such that the image of any triangle (as its polygonal line) is a square. Show that f(π)f(\pi) is a square.
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