public static long Solution1()
{
long solution = 0;
long power = UtilityFunctions.IntegralPower(2, order) - 1;
var primes = UtilityFunctions.Primes(UtilityFunctions.IntegralPower(2, order / 4));
var primeFactors = new List <long>();
var ordersModP = new List <long>();
var powersOfTwo = new Dictionary <long, long>();
bool keyAdded = false;
var factors = new Dictionary <long, long>();
for (int i = 2; i <= Math.Sqrt(order); i++)
{
if (order % i == 0)
{
powersOfTwo.Add(i, UtilityFunctions.IntegralPower(2, i) - 1);
if (i * i != order)
{
powersOfTwo.Add(order / i, UtilityFunctions.IntegralPower(2, order / i) - 1);
}
}
}
var keys = powersOfTwo.Keys.OrderBy(t => t).ToArray();
foreach (var p in primes)
{
if (power < p * p)
{
keyAdded = false;
primeFactors.Add(power);
foreach (var key in keys)
{
if (powersOfTwo[key] % power == 0)
{
keyAdded = true;
ordersModP.Add(key);
break;
}
}
if (!keyAdded)
{
ordersModP.Add(order);
}
break;
}
var primePower = p;
while (power % p == 0)
{
keyAdded = false;
primeFactors.Add(p);
foreach (var key in keys)
{
if (powersOfTwo[key] % primePower == 0)
{
keyAdded = true;
ordersModP.Add(key);
break;
}
}
if (!keyAdded)
{
ordersModP.Add(order);
}
power /= p;
primePower *= p;
}
}
factors.Add(1, 1);
for (int i = 0; i < primeFactors.Count; i++)
{
keys = factors.Keys.ToArray();
foreach (var key in keys)
{
var newKey = key * primeFactors[i];
if (!factors.ContainsKey(newKey))
{
factors.Add(newKey, UtilityFunctions.Lcm(factors[key], ordersModP[i]));
}
}
}
foreach (var factor in factors)
{
if (factor.Value == order)
{
solution += factor.Key + 1;
}
}
return(solution);
}
