/// <summary>
/// For right triangles, using Euclid formula, modified function for problem75
/// </summary>
/// <param name="p">Triangle perimeter</param>
/// <returns></returns>
private static int GetSingularPythagoreanTriples(long p)
{
var count = 0;
var bound = (long)Math.Sqrt(p / 2);
long m;
for (m = 2; m <= bound; m++)
{
if ((p / 2) % m == 0)
{ // m found
long k;
if (m % 2 == 0)
{ // ensure that we find an odd number for k
k = m + 1;
}
else
{
k = m + 2;
}
while (k < 2 * m && k <= p / (2 * m))
{
if (p / (2 * m) % k == 0 && UtilityMath.EuclidianGCD(k, m) == 1)
{
long d = p / 2 / (k * m);
long n = k - m;
long a = d * (m * m - n * n);
long b = 2 * d * n * m;
long c = d * (m * m + n * n);
if (a + b + c == p)
{
count++;
}
// only consider those which only have one combination
if (count > 1)
{
return(0);
}
}
k += 2;
}
}
}
return(count);
}