/// <summary>
/// 计算欧拉函数Φ(m), 即0与m之间与m互素的整数个数
/// </summary>
/// <param name="number"></param>
/// <param name="relativePrimes"></param>
/// <returns></returns>
public static long GetRelativelyPrimeCount(long number, out List <long> relativePrimes)
{
relativePrimes = new List <long>();
if (number < 1)
{
throw new ArgumentException("Number should be positive integers.");
}
for (long i = 1; i <= number; i++)
{
var gcd = GCD.GetGCD(i, number);
if (gcd == 1)
{
relativePrimes.Add(i);
}
}
return(relativePrimes.Count);
}
public List <long> GetSolution()
{
long gcd = GCD.GetGCD(_a, _m);
if (_c % gcd != 0)
{
Console.WriteLine("gcd(a, m) can't divide c, this congruence has no solution.");
return(null);
}
var solution = GCD.GetSolution_LinearAxBy(_a, _m);
if (solution == null)
{
Console.WriteLine("Solution of ax + my = gcd(a, m) is null.");
return(null);
}
long factor = _c / gcd;
long u0 = solution[0];
long x0 = factor * u0;
long factor2 = _m / gcd;
List <long> result = new List <long>();
for (int i = 0; i < gcd; i++)
{
var temp = x0 + i * factor2;
if (temp >= _m)
{
temp = temp % _m;
}
if (temp < 0)
{
temp = _m - Math.Abs(temp) % _m;
}
result.Add(temp);
}
return(result);
}
