a geometrical problem with a number teory flavour
Source: bmo 1991
April 23, 2007
geometrynumber theoryrelatively primegeometry open
Problem Statement
Show that there are infinitely many noncongruent triangles which satisfy the following conditions:
i) the side lengths are relatively prime integers;
ii)the area is an integer number;
iii)the altitudes' lengths are not integer numbers.