Problem 482
The incenter of a triangle
ABC is an integer sided triangle with incenter I and perimeter p.
The segments IA, IB and IC have integral length as well.
Let L = p + |IA| + |IB| + |IC|.
Let S(P) = ∑L for all such triangles where p ≤ P. For example, S(103) = 3619.
Find S(107).
三角形的内心
三角形ABC的三边长都是整数，其内心记为I，周长记为p.
连接内心和顶点的线段IA，IB和IC的长度恰好也都是整数。
记L = p + |IA| + |IB| + |IC|。
对于所有满足p ≤ P的三角形，记S(P) = ∑L。例如，S(103) = 3619。
求S(107)。