My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too. Or just jump to my GitHub repository.

       
#include <iostream>
       
#include <vector>
       
 
       
// ---------- 32 bit powmod from my toolbox ----------

       
 
       
// return (base^exponent) % modulo for 32-bit values, no need for mulmod

       
unsigned int powmod(unsigned int base, unsigned int exponent, unsigned int modulo)
       
{
       
  unsigned int result = 1;
       
  while (exponent > 0)
       
  {
       
    // fast exponentation:
       
    // odd exponent ? a^b = a*a^(b-1)
       
    if (exponent & 1)
       
      result = (result * (unsigned long long)base) % modulo;
       
 
       
    // even exponent ? a^b = (a*a)^(b/2)
       
    base = (base * (unsigned long long)base) % modulo;
       
    exponent >>= 1;
       
  }
       
  return result;
       
}
       
 
       
// ---------- problem specific code ----------

       
 
       
// try every possible exponent ... takes many minutes per number

       
unsigned int bruteForce(unsigned int n, unsigned int modulo)
       
{
       
  unsigned int result = modulo;
       
  while (result > 1)
       
  {
       
    result--;
       
    if (powmod(n, result, modulo) == result)
       
      break;
       
    if (result % 1000000 == 0)
       
      std::cout << n << " " << result << std::endl;
       
  }
       
  return result;
       
}
       
 
       
// find maximum exponent e such that n^e = e mod modulo

       
unsigned int search(unsigned int n, unsigned int modulo)
       
{
       
  unsigned int exponent = n;
       
  do
       
  {
       
    auto next = powmod(n, exponent, modulo);
       
    // stuck in a loop => we're finished
       
    if (next == 0 || next == exponent)
       
      return next;
       
 
       
    // keep going ...
       
    exponent = next;
       
  } while (true);
       
}
       
 
       
int main()
       
{
       
  unsigned int limit = 1000000;
       
  std::cin >> limit;
       
 
       
  const unsigned int Modulo = 1000000000;
       
 
       
  //std::cout << bruteForce(4, Modulo) << std::endl;
       
 
       
  unsigned long long sum = 0;
       
  for (unsigned int i = 2; i <= limit; i++)
       
    sum += search(i, Modulo);
       
 
       
  std::cout << sum << std::endl;
       
  return 0;
       
}

This solution contains 12 empty lines, 11 comments and 2 preprocessor commands.