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Problem 482


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)。