MathDB

Semiperimeter, inradius of triangle with int side lengths

Source: IMO Shortlist 2000, N5

August 10, 2008

Diophantine equationnumber theoryinradiusperimeterTriangleIMO Shortlist

Problem Statement

Prove that there exist infinitely many positive integers

n

such that p \equal{} nr, where

p

and

r

are respectively the semiperimeter and the inradius of a triangle with integer side lengths.