public static long Solution()
{
var stopwatch = new Stopwatch();
long solution = 1;
var exponents = new List <int>();
var primes = UtilityFunctions.Primes(7376512);
var candidates = new List <long> {
1
};
for (int i = 0; i < primes.Count; i++)
{
var primePower = primes[i] * primes[i];
var maxCandidate = candidates.Max();
if (primePower > primes.Last() && primePower > maxCandidate)
{
break;
}
while (primePower < Math.Max(primes.Last(), maxCandidate))
{
candidates.Add(primePower);
if (maxCandidate > primes.Last())
{
candidates.Remove(maxCandidate);
maxCandidate = candidates.Max();
}
else
{
primes.RemoveAt(primes.Count - 1);
}
primePower *= primePower;
}
}
foreach (var t in candidates.Concat(primes))
{
solution = (solution * t) % 500500507;
}
Console.WriteLine($"Time spent finding max {stopwatch.ElapsedMilliseconds}");
return(solution);
}
public static long Solution()
{
long solution = 0;
var primes = UtilityFunctions.Primes(limit / 2);
for (int i = 0; i < primes.Count; i++)
{
var p = primes[i];
List <long> powersOfP = new List <long>();
var n = p;
while (n < limit / p)
{
powersOfP.Add(n);
n *= p;
}
for (int j = i + 1; j < primes.Count; j++)
{
var q = primes[j];
if (p * q > limit)
{
break;
}
var powersOfPTimesQ = new List <long>(powersOfP);
long max = 0;
while (true)
{
powersOfPTimesQ = powersOfPTimesQ.Where(t => t * q <= limit).Select(t => t * q).ToList();
if (powersOfPTimesQ.Count == 0)
{
break;
}
max = Math.Max(powersOfPTimesQ.Max(), max);
}
solution += max;
}
}
return(solution);
}
public static long Solution()
{
long solution = 0;
long mLimit = (long)1e4;
HashSet <long> squares = new HashSet <long>();
for (long m = 2; m < mLimit; m++)
{
long kLimit = (long)Math.Sqrt(limit / (m * m * m) + 1);
var step = 2 - (m % 2);
for (long r = 1; r < m; r += step)
{
if (UtilityFunctions.Gcd(m, r) != 1)
{
continue;
}
if (m * m * m * r + r * r >= limit)
{
break;
}
for (long k = 1; k <= kLimit; k++)
{
long n = k * k * m * m * m * r + k * r * r;
if (n >= limit)
{
break;
}
if (UtilityFunctions.IsPerfectSquare(n))
{
if (!squares.Contains(n))
{
solution += n;
squares.Add(n);
}
}
}
}
}
return(solution);
}
public static long Solution()
{
long solution = 0;
HashSet <long> strongTruncatableHarshads;
var rightTruncatableHarshads = RightTruncatableHarshads(limit, out strongTruncatableHarshads);
foreach (var s in strongTruncatableHarshads)
{
foreach (var i in new[] { 1, 3, 7, 9 })
{
var n = 10 * s + i;
if (UtilityFunctions.IsPrime(n))
{
solution += n;
}
}
}
return(solution);
}
public static long Solution()
{
long solution = 0;
var primes = UtilityFunctions.Primes(limit + 100);
for (int i = 3; true; i++)
{
var p1 = primes[i - 1];
var p2 = primes[i];
if (p1 > limit)
{
break;
}
long powerOf10 = (long)Math.Pow(10, p1.ToString().Length);
var x = (-p1 * UtilityFunctions.ModularInverse(powerOf10, p2) % p2 + p2) % p2;
solution += powerOf10 * x + p1;
}
return(solution);
}
public static long Solution()
{
long solution = 0;
for (int a = 1; a <= limit; a++)
{
for (int c = 1; c <= a; c++)
{
for (int b = 1; b <= limit; b++)
{
for (int d = 1; d <= b; d++)
{
var internalPoints =
((a + c) * (b + d)
- UtilityFunctions.Gcd(a, b)
- UtilityFunctions.Gcd(b, c)
- UtilityFunctions.Gcd(c, d)
- UtilityFunctions.Gcd(d, a)) / 2 + 1;
if (UtilityFunctions.IsPerfectSquare(internalPoints))
{
solution += 4;
if (a == c || b == d)
{
solution -= 2;
if (a == c && b == d)
{
solution -= 1;
}
}
}
}
}
}
}
return(solution);
}
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 Solution()
{
long solution = 0;
var primes = UtilityFunctions.Primes(limit);
foreach (var p in primes)
{
var ord = UtilityFunctions.MultiplicativeOrder(10, 9 * p);
if (ord == 0)
{
solution += p;
continue;
}
while (ord % 2 == 0 || ord % 5 == 0)
{
if (ord % 2 == 0)
{
ord /= 2;
}
if (ord % 5 == 0)
{
ord /= 5;
}
}
if (ord > 1)
{
solution += p;
}
else
{
Console.WriteLine(p);
}
}
return(solution);
}
public static long Solution()
{
long solution = 0;
var counter = 0;
var stopwatch = new Stopwatch();
stopwatch.Start();
var previousTime = 0.0;
var currentTime = 0.0;
var primes = UtilityFunctions.Primes(1000000);
currentTime = stopwatch.ElapsedMilliseconds;
Console.WriteLine($"Settig up took {currentTime - previousTime} milliseconds.");
previousTime = currentTime;
foreach (var p in primes)
{
var order = UtilityFunctions.MultiplicativeOrder(10, 9 * p);
if (order == 0)
{
continue;
}
if (limit % order == 0)
{
solution += p;
counter += 1;
Console.WriteLine(p);
if (counter >= 40)
{
return(solution);
}
}
}
return(solution);
}
internal static long PandigitalPrimeSets(List <long> digits)
{
if (digits.Count == 0)
{
return(1);
}
long count = 0;
digits.Sort();
var maxElement = digits[digits.Count - 1];
var restOfDigits = UtilityFunctions.Complement(new List <long> {
maxElement
}, digits);
var subsets = UtilityFunctions.GenerateSubsets(restOfDigits);
foreach (var subset in subsets)
{
subset.Add(maxElement);
var complement = UtilityFunctions.Complement(subset, digits);
var subsetDigitSignature = UtilityFunctions.DigitSignature(subset, ProblemDigits);
count += PrimeCandidates[subsetDigitSignature].Count * PandigitalPrimeSets(complement);
}
return(count);
}
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);
}
public static long SolutionOld()
{
long answer = 0;
var validPairs = new Dictionary <long, HashSet <long> >();
var validSums = new HashSet <long>();
for (long p = 2; p < limit; p++)
{
for (long q = 1; q < p; q++)
{
if (p + q > limit)
{
break;
}
if (p % 2 == 1)
{
if ((q % 2 == 1) && (p * q) % 4 != 3)
{
continue;
}
if (q % 4 == 2)
{
continue;
}
}
else
{
if ((p % 4 == 2) && (q % 2 == 1))
{
continue;
}
}
var aSquare = (p * p + q * q + p * q);
if (!UtilityFunctions.IsPerfectSquare(aSquare))
{
continue;
}
if (validPairs.ContainsKey(p))
{
validPairs[p].Add(q);
if (validPairs.ContainsKey(q))
{
long sum = long.MaxValue;
foreach (var r in validPairs[q])
{
if (validPairs[p].Contains(r))
{
var bSquare = p * p + r * r + p * r;
var cSquare = r * r + q * q + r * q;
if (bSquare + cSquare < aSquare)
{
var bc = Math.Sqrt(bSquare * cSquare);
if (bSquare + cSquare + bc < aSquare)
{
continue;
}
}
sum = p + q + r;
if (sum < limit)
{
validSums.Add(sum);
Console.WriteLine($"{p} {q} {r} {sum}");
}
}
}
}
}
else
{
validPairs.Add(p, new HashSet <long> {
q
});
}
}
}
foreach (var sum in validSums)
{
answer += sum;
}
return(answer);
}
public static long Solution()
{
long answer = 0;
var validPairs = new Dictionary <long, HashSet <long> >();
var validSums = new HashSet <long>();
for (long m = 2; m < limit; m++)
{
var stepSize = 2 - (m % 2);
for (long n = 1; n < m; n += stepSize)
{
if (UtilityFunctions.Gcd(m, n) != 1 || (m - n % 3) == 0)
{
continue;
}
var firstSide = 2 * m * n + n * n;
var secondSide = m * m - n * n;
if (m * m + 2 * m * n > limit)
{
break;
}
var p = Math.Max(firstSide, secondSide);
var q = Math.Min(firstSide, secondSide);
for (long k = 1; k < limit; k++)
{
if (k * (p + q) > limit)
{
break;
}
if (validPairs.ContainsKey(k * p))
{
validPairs[k * p].Add(k * q);
}
else
{
validPairs.Add(k * p, new HashSet <long> {
k *q
});
}
}
}
}
foreach (var p in validPairs.Keys)
{
foreach (var q in validPairs[p])
{
if (validPairs.ContainsKey(q))
{
long sum = long.MaxValue;
foreach (var r in validPairs[q])
{
if (validPairs[p].Contains(r))
{
var aSquare = p * p + q * q + p * q;
var bSquare = p * p + r * r + p * r;
var cSquare = r * r + q * q + r * q;
if (bSquare + cSquare < aSquare)
{
var bc = Math.Sqrt(bSquare * cSquare);
if (bSquare + cSquare + bc < aSquare)
{
continue;
}
}
sum = p + q + r;
if (sum < limit)
{
validSums.Add(sum);
Console.WriteLine($"{p} {q} {r} {sum}");
}
}
}
}
}
}
foreach (var sum in validSums)
{
answer += sum;
}
return(answer);
}
private static bool IsHarshad(long n)
{
var digitSum = UtilityFunctions.DigitSum(n);
return(n % digitSum == 0);
}
public static double Solution()
{
return(7 * (1 - UtilityFunctions.Choose(60, 20) / (double)UtilityFunctions.Choose(70, 20)));
//return ExpectedBalls(0,0);
}