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Find all Pythagorean triangles with length or height less than or equal to 20

Pythagorean triangles are right angle triangles whose sides comply with the following equation:

a * a + b * b = c * c

where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. Find all such triangles where a, b and c are non-zero integers with a and b less than or equal to 20. Sort your results by the size of the hypotenuse. The expected answer is:

[3, 4, 5]
[6, 8, 10]
[5, 12, 13]
[9, 12, 15]
[8, 15, 17]
[12, 16, 20]
[15, 20, 25]
java
SortedSet<List<Integer>> results = new TreeSet<List<Integer>>(new Comparator<List<Integer>>() {
public int compare(List<Integer> o1, List<Integer> o2) {
return o1.get(2).compareTo(o2.get(2));
}
});
for (int x = 1; x <= 20; x++) {
for (int y = 1; y <= 20; y++) {
double z = Math.hypot(x, y) ;
if ((int) z == z)
results.add(Arrays.asList( new Integer[] { x, y, (int) z }));
}
}

Greatest Common Divisor

Find the largest positive integer that divides two given numbers without a remainder. For example, the GCD of 8 and 12 is 4.

java
static int gcd(int a, int b) {
if (Math.min(a, b) == 0)
return Math.max(a, b);
else
return gcd(Math.min(a, b), Math.abs(a - b));
}
csharp
public static int gcd(int a, int b)
{
if (b == 0)
return a;
else
return gcd(b, a % b);
}