Project Euler > Problem 39 > Integer right triangles (Java Solution)

Problem:

If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.

{20,48,52}, {24,45,51}, {30,40,50}

For which value of p [≤] 1000, is the number of solutions maximised?

Solution:

840

Code:
The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}

/* 
 * Solution to Project Euler problem 39
 * By Nayuki Minase
 * 
 * http://nayuki.eigenstate.org/page/project-euler-solutions
 * https://github.com/nayuki/Project-Euler-solutions
 */


public final class p039 implements EulerSolution {
 
 public static void main(String[] args) {
  System.out.println(new p039().run());
 }
 
 
 public String run() {
  int maxPerimeter = 0;
  int maxTriangles = 0;
  for (int p = 1; p <= 1000; p++) {
   int triangles = countSolutions(p);
   if (triangles > maxTriangles) {
    maxTriangles = triangles;
    maxPerimeter = p;
   }
  }
  return Integer.toString(maxPerimeter);
 }
 
 
 private static int countSolutions(int p) {
  int count = 0;
  for (int a = 1; a <= p; a++) {
   for (int b = a; b <= p; b++) {
    int c = p - a - b;
    if (b <= c && a * a + b * b == c * c)
     count++;
   }
  }
  return count;
 }
 
}