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Problem 513


Problem 513


Integral median

ABC is an integral sided triangle with sides a≤b≤c.
mc is the median connecting C and the midpoint of AB.
F(n) is the number of such triangles with c≤n for which mc 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。
mc是连接C与AB边中点的中线。
若同时还满足c≤n且mc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)。