CLASS IDENTITEREMARQUABLE.JAVA

public class IdentiteRemarquable
{
	/**
	 * This method enable to calculate factorial
	 * @param
	 *	n - n!
	 */
	public static long factoriel(int n)
	{
		return n < 1 ? 1 : n * factoriel(--n);
	}

	/*
	 * This method enable to calculate a combinaison with n <= k
	 * C (n,k) = k! / (n!(k-n)!)
	 */
	public static long combinaison(int n, int k)
	{
		return (factoriel(k) / (factoriel(n) * (factoriel(k-n))));
	}

	/**
	 * This method enable to calculate (a+b)^n
	 * (a+b)^n = Sum( C(n,k) * a^k * b^(n-k) )	
	 */
	public static long calculate(int a, int b, int n)
	{
		long out = 0;

		for (int k = 0; k <= n; k++)
		{
			out += combinaison(k, n) * Math.pow((double)a, (double)k) * Math.pow((double)b, (double)(n - k)); 
		}

		return out;
	}


	/**
	 * Test program
	 */
	public static void main(String[] args)
	{
		// factoriel
		int f = 5;
		long resultF = IdentiteRemarquable.factoriel(f);

		System.out.println("f(" + f + ") = " + resultF); // fact(5) = 120

		// combinaison
		int n = 3;
		int k = 17;
		long c = IdentiteRemarquable.combinaison(n, k);

		System.out.println("c(" + n + "," + k + ") = " + c); // C (3,17) = 680

		// (a+b)^n
		int a = 5;
		int b = 2;
		int n2 = 2;
		long r = IdentiteRemarquable.calculate(a, b, n2);

		System.out.println("(" + a + "+" + b + ")^" + n2 + " = " + r); // (5+2)^2 = 49

		System.out.println(IdentiteRemarquable.calculate(12, 7, 10)); // (12 + 7)^10 = ... 

	}
}