# Testing 10 digit numbers

**Number Theory**Level 5

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 \(N\)?