Counting Integer Perimeters

★ 6/10plane geometry number theory Counting Triangle Geometry

Problem

In triangle $QRS$ , the bisector of angle $QRS$ meets $QS$ at $T$ . Let $QT = m$ and $TS = n$ , where $m, n$ are positive integers with $n > m$ . Suppose the perimeter $p$ of triangle $QRS$ is an integer, and the number of possible values of $p$ is $m^2 + 2m - 1$ . Find $n - m$ .

Answer

Solution

Difficulty	6/10
Topics	plane geometry, number theory, Counting, Triangle Geometry

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