Problem #75 says:

It turns out that 12 cm is the smallest length of wire that can be bent to form an integer
sided right angle triangle in exactly one way, but there are many more examples.

12 cm: (3,4,5)
24 cm: (6,8,10)
30 cm: (5,12,13)
36 cm: (9,12,15)
40 cm: (8,15,17)
48 cm: (12,16,20)

In contrast, some lengths of wire, like 20 cm, cannot be bent to form an integer sided right
angle triangle, and other lengths allow more than one solution to be found; for example,
using 120 cm it is possible to form exactly three different integer sided right angle triangles.

120 cm: (30,40,50), (20,48,52), (24,45,51)

Given that L is the length of the wire, for how many values of L ≤ 1,500,000 can exactly
one integer sided right angle triangle be formed?

Another counting problem but here we have to avoid duplicate entries that can come from a variety
of places. This solution uses the 2 number approach for generating Pythagorean triples, which it then finds
the lengths of the triple and catalogs it in an array to track duplicates, Then counts all the values of the
array that equal 1 for the final answer.

Solution is provided in c#/mono. Runs in under one second.

using System;
using System.Collections;
using System.Diagnostics;

namespace Problem75
{
	class MainClass
	{
		public static void Main (string[] args)
		{
			Stopwatch sw = new Stopwatch();
			sw.Start();
			int limit = 1500000;
			int adjlimit = (int)(Math.Sqrt((float)limit));
			ArrayList tri = new ArrayList(limit);

			for (int st = 0; st < limit+1; st++)
				tri.Add(0);

			for (int i = 1; i <= adjlimit; i=i+2)
			{
				for (int j = 2; j<= adjlimit; j=j+2)
				{
					if (GCD(i,j) == 1)
					{
						int sum = Math.Abs((j*j) - (i*i)) + (2*j*i) + ((i*i) + (j*j));
						for (int s = sum; s < limit; s=s+sum)
						{

							tri[s] = (int)tri[s]+1;
						}
					}
				}
			}
			Console.WriteLine(TallyResults(tri));
			sw.Stop();
			Console.WriteLine(sw.Elapsed);
			Console.ReadLine();
		}
		public static int TallyResults(ArrayList a)
		{
			int RetVal = 0;
			foreach (int i in a)
			{
				if (i == 1)
					RetVal= RetVal+1;
			}
			return RetVal;
		}
		public static int GCD (int a, int b)
		{
			if (b == 0)
				return a;
			else
				return GCD(b,(a%b));
		}
	}
}