<begin> For a triangle with integer sides a,b,c (none over 2000) evaluate the triplet of its medians m_a , m_b , m_c .
Let those three become sides of a new triangle i.e. (a,b,c) =(m_a , m_b , m_c ).
<end>

It is up to you to find a triplet (a,b,c) such that the above procedure can be executed a maximal number of times, creating sets of “medians“ with integer values only.

The answer should include: (a,b,c) and all interim sets of medians.

Rem: Can be solved analytically.

(In reply to Solution by Dej Mar)

Am I missing the point here? An equilateral triangle with integer sides can never have medians with integer lengths. Shouldn't we be looking for triangles whose median lengths are integers rather than triangles whose sides have mid points that form the vertices of a triangle with integer sides?

Edited on December 21, 2014, 8:49 am

Edited on December 22, 2014, 10:17 am

Posted by Harry on 2014-12-20 18:24:16