problem045.java

package project_beuler;

public class problem045 {
	
//	Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
//
//	Triangle	 	Tn=n(n+1)/2	 	1, 3, 6, 10, 15, ...
//	Pentagonal	 	Pn=n(3n−1)/2	 	1, 5, 12, 22, 35, ...
//	Hexagonal	 	Hn=n(2n−1)	 	1, 6, 15, 28, 45, ...
//	It can be verified that T285 = P165 = H143 = 40755.
//
//	Find the next triangle number that is also pentagonal and hexagonal.

	public static void main(String[] args) {
		// TODO Auto-generated method stub
//		a(a+1)/2
//		b(3b-1)/2
//		c(2c-1)
//		a(a+1) = b(3b-1) = c(2c-1)
		for(long a = 286; true; a++) {
			long b; long c;
			for(b = a; b*(3*b-1) > a*(a+1); b--);
			if(a*(a+1) != b*(3*b-1)) continue;
			for(c = b; c*(2*c-1) > b*(3*b-1)/2; c--);
			if(b*(3*b-1)/2 == c*(2*c-1)) {
				System.out.println(c*(2*c-1));
				break;
			}
		}
	}
	

}