package problem09;

/*

Special Pythagorean triplet

Problem 9

A Pythagorean triplet is a set of three natural numbers, a b c, for which,

a^2 + b^2 = c^2

For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.

There exists exactly one Pythagorean triplet for which a + b + c = 1000.

Find the product abc.

*/

public class PythagoreanTriplet {

public static void main(String[] args) {

int a = 0, b = 0, c = 0;

while (a + b + c != 1000) {

for (int cSquared = 1; cSquared <= 1000000; cSquared++) {

if (Math.sqrt((double) cSquared) % 1 == 0.0) {

c = (int) Math.sqrt(cSquared); // finds cSquared for all c up to 1000

for (int j = 1; j < c; j++) {

for (int k = 1; k < j; k++) {

if ((j * j) + (k * k) == cSquared) {

a = j;

b = k;

if (a + b + c == 1000) {

System.out.println("a = " + a + " b = " + b + " c = " + c);

System.out.println("a * b * c = " + a * b * c);

k = j;

j = c;

cSquared = 1000001;

}

}

}

}

}

}

} // end of while

} // end of main method

} // end of pythagoreanTriplet