BMO Shortlist 2021 N7
Source: BMO Shortlist 2021
May 8, 2022
Balkanshortlist2021number theoryTriangle
Problem Statement
A super-integer triangle is defined to be a triangle whose lengths of all sides and at least
one height are positive integers. We will deem certain positive integer numbers to be good with
the condition that if the lengths of two sides of a super-integer triangle are two (not necessarily
different) good numbers, then the length of the remaining side is also a good number. Let be
a good number. Prove that all integers larger than are good numbers.