<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 re: Solution by Harry)

As I understood the problem, Harry. Ady was inferring the points intersected by the medians with the sides of the triangle (the medial points) would be the vertices of the inner triangle.

Edited on December 20, 2014, 6:48 pm

Posted by Dej Mar on 2014-12-20 18:47:24