Problem 1

public class P45 {

    public static void main(String[] args) {
        long H = 0;
        long i = 144;
        while(true) {
            H = i*((i<<1)-1);
            if ( isPentagonal(H) && isTriangle(H) ) {
                break;
            }
            i++;
        }
        System.out.println(H);
    }

    private static boolean isPentagonal(long x) {
        double n = (1 + Math.sqrt(24*x+1)) / 6;
        return n == (long)n;
    }

    private static boolean isTriangle(long x) {
        double n = (-1 + Math.sqrt((x<<3)+1)) / 2;
        return n == (long)n;
    }

}