public static long Solution()
{
long solution = 0;
for (long i = 2; i <= limit; i++)
{
if ((i % 2) == 0)
{
var k = i / 2;
solution += UtilityFunctions.IntegralPower(30, k - 1) * 20;
}
// else if(i%4 == 1)
// {
// var k = (i - 1) / 4;
// solution += UtilityFunctions.IntegralPower(600, k) * 5;
// }
else if (i % 4 == 3)
{
var k = (i + 1) / 4;
solution += UtilityFunctions.IntegralPower(500, k - 1) * 100;
}
}
return(solution);
}
public static double Solution()
{
double solution = 0;
double peter = 0;
long colin = 0;
long totalColin = 0;
long totalPeter = 0;
var peterCount = (double)UtilityFunctions.IntegralPower(4, 9);
var colinCount = (double)UtilityFunctions.IntegralPower(6, 6);
for (int n = 36; n >= 6; n--)
{
colin = DieRolls(n, 6, 6);
totalColin += colin;
solution += (colin / colinCount) * (peter);
var tempPeter = DieRolls(n, 9, 4);
totalPeter += tempPeter;
peter += tempPeter / peterCount;
}
return(solution);
}
private static double[][] GenerateRandomGrid(int size)
{
var numberOfRandoms = size * (size + 1) / 2;
var randoms = new double[size][];
double t = 0;
for (int k = 1; k <= size; k++)
{
randoms[k - 1] = new double[k];
for (int j = 1; j <= k; j++)
{
t = (615949 * t + 797807) % UtilityFunctions.IntegralPower(2, 20);
randoms[k - 1][j - 1] = t - UtilityFunctions.IntegralPower(2, 19);
}
}
return(randoms);
}
public static long Solution()
{
var stopwatch = new System.Diagnostics.Stopwatch();
long solution = 0;
var divisorsOfOrder = UtilityFunctions.Divisors(order);
var primes = UtilityFunctions.Primes((int)Math.Sqrt(UtilityFunctions.IntegralPower(2, order / 2) + 1));
var primeFactors = UtilityFunctions.PrimeFactors(UtilityFunctions.IntegralPower(2, order) - 1, primes);
var reducedPrimes = primeFactors.Select(t => t.Item1).ToList();
foreach (var d in divisorsOfOrder)
{
var m = UtilityFunctions.Moebius(d, null, primes);
if (m != 0)
{
var divisorsOfPowerOfTwo = UtilityFunctions.Divisors(UtilityFunctions.IntegralPower(2, order / d) - 1, null, reducedPrimes);
solution += (divisorsOfPowerOfTwo.Sum() + divisorsOfPowerOfTwo.Count()) * m;
}
}
return(solution);
}
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);
}
