/* 
   looks for pairs of natural numbers x, y such that 
   x^2 + y^2 = z^2
   with z natural
   
   All pairs x < y <= mxn are tested
*/

import java.util.Hashtable;

public class Equazioni
{
	static Hashtable ratioes = new Hashtable();

	public static String toString(long a, long b) {
		return a+","+b;
	}
	
	public static long MCD(long a, long b) { // a e b qualsiasi
		a = Math.abs(a);
		b = Math.abs(b);
		if(a>=b)
			return calcolaMCDEuclide(a, b);
		else
			return calcolaMCDEuclide(b, a);
	
	}
	
	
	public static long calcolaMCDEuclide(long a, long b) { // assumo a >= b
		while(b!=0) {
			long resto = a%b;
			a = b;
			b = resto;
		}
		return a;
	}
		
	public static boolean add(long a, long b)
	{
		long ar, br;
		long mcd = MCD(a,b);
		ar = a/mcd;
		br = b/mcd;
		String s = toString(ar, br);
		if(ratioes.get(s) == null) {
			ratioes.put(s, s);
			return true;
		}
		return false;
	}

	public static void main(String[] args)
	{
		if(args.length != 1) {
			System.out.println("Usage: java Equazioni maxn\n      where maxn is the maximum value to be tested for\n");
			System.exit(0);
		}
		long max = Integer.parseInt(args[0]);
		long n = 0;
		System.out.printf("    n     |  cateto1  |  cateto2  |  ipotenusa\n----------+-----------+-----------+-------------\n");
		for(long x=1; x<max; x++)
		{
			for(long y=x; y<max; y++)
			{
				long sommaQuad = x*x + y*y;
				long rad = (long) (Math.sqrt(sommaQuad));
				if(
					( sommaQuad == rad*rad || sommaQuad == (rad+1)*(rad+1) )
					&&
					add(x,y)
				   ) {
				   		n++;
						System.out.printf("%8d  |%9d  |%9d  |%11d\n", n, x, y, rad);
					}
			}
		}
		System.out.println("trovate "+n+" coppie");
	}
}