Problem 513

Integral median

ABC is an integral sided triangle with sides a≤b≤c.
m_c is the median connecting C and the midpoint of AB.
F(n) is the number of such triangles with c≤n for which m_c has integral length as well.
F(10)=3 and F(50)=165.

Find F(100000).

整数长度的中线

三角形ABC是一个三边长a≤b≤c均为整数的三角形。
m_c是连接C与AB边中点的中线。
若同时还满足c≤n且m_c长度也为整数，记这样的三角形总数为F(n)。
已知F(10)=3以及F(50)=165。

求F(100000)。