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Triangles with Integer Sides

Source: 2012 IrMO Paper 1 Problem 4

February 16, 2018
number theory

Problem Statement

There exists an infinite set of triangles with the following properties:
(a) the lengths of the sides are integers with no common factors, and
(b) one and only one angle is 60āˆ˜60^\circ.
One such triangle has side lengths 5,7,85,7,8. Find two more.
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