private static long GetSmallestMultiple(IEnumerable <int> numbers)
{
long smallestMultiple = 1;
var listOfFactorizations = numbers.Select(number => PrimeHelper.GetPrimeFactorization(number));
Dictionary <int, int> factorizationOfAnswer = GetPrimeFactorizationOfSmallestMultiple(listOfFactorizations);
foreach (var key in factorizationOfAnswer.Keys)
{
smallestMultiple *= (long)Math.Pow(key, factorizationOfAnswer[key]);
}
return(smallestMultiple);
}
public void GetPrimeFactorization_18_ReturnsExpectedDictionary()
{
// Arrange
var number = 18;
var expectedDictionary = new Dictionary <int, int>
{
[2] = 1,
[3] = 2
};
// Act
var result = PrimeHelper.GetPrimeFactorization(number);
// Assert
result.Should().BeEquivalentTo(expectedDictionary);
}
private static BigInteger CalculatePrimitiveRoot(BigInteger p)
{
// Check if p is prime or not
if (!PrimeHelper.IsProbablePrime(p))
{
throw new ArgumentException($"Parameter {nameof(p)} must be a prime number.", nameof(p));
}
BigInteger phi = p - 1; // The Euler Totient function phi of a prime number p is p-1
IEnumerable <BigInteger> primeFactors = PrimeHelper.GetPrimeFactorization(phi).Distinct();
List <BigInteger> powersToTry = primeFactors.Select(factor => phi / factor).ToList();
for (int r = 2; r <= phi; r++) // Check for every number from 2 to phi
{
if (powersToTry.All(n => BigInteger.ModPow(r, n, p) != 1)) // If there was no n such that r^n ≡ 1 (mod p)
{
return(r); // We found our primitive root
}
}
throw new Exception($"No primitive root found for prime {p}!"); // If no primitive root found
}