# Testing 10 digit numbers

For any given integer $$m,$$ define a sequence of integers as follows. $x_{0,m} =m;\ x_{i+1, m}=x_{i,m}^2+2x_{i,m},\ i=0,1,2,...$

Let $$N$$ be the sum of all integer $$3\leq n \leq 10^{10}$$ such that $$x_{n,m}$$ is divisible by $$n$$ for every integer $$m,$$ $$1\leq m\leq n-2.$$

What are the last 3 digits of $$N$$?

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