## Problem Description :

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^2 + b^2 = c^2
For example, 32 + 42 = 9 + 16 = 25 = 52. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

## Concept :

We have following two equations.

1) a^2+b^2=c^2
2) a+b+c=1000

on solving these equations mathematically.

1<=a<=999
b=(1000^2-(2*a*1000))/(2*(1000-a))
c=1000-b-a

## Java Program :

```package com.javamultiplex.projecteuler;

/**
*
* @author Rohit Agarwal
* @category Project Euler Problems
* @problem Problem 9
*
*/
public class Problem9 {

public static void main(String[] args) {

int limit = 1000, a, b, c, result;
for (int i = 1; i < limit; i++) {
a = i;
/*
* if a+b+c=n and c^2=a^2+b^2 on solving above equations we can find
* value of b in terms of a and n b=(n^2-2an)/2(n-a)
*
*/
b = (int) ((Math.pow(limit, 2) - 2 * a * limit) / (2 * (limit - a)));
c = limit - b - a;
if (isPythagoreanTriplet(a, b, c)) {
if (a + b + c == limit) {
result = a * b * c;
System.out.println("Pythagorean triplet for which a + b + c = 1000 is : " + result);
break;
}
}
}

}

//a,b and c are Pythagorean Triplets if c>b>a and c^2=a^2+b^2
private static boolean isPythagoreanTriplet(int a, int b, int c) {

boolean result = false;
if (c > b && b > a) {
if (c * c == a * a + b * b) {
result = true;
}
}
return result;
}

}
```

## Output :

 Output - Project Euler Problem 9 Solution in Java

## References :

https://projecteuler.net/problem=9

https://en.wikipedia.org/wiki/Pythagorean_triple

https://docs.oracle.com/javase/7/docs/api/java/lang/Math.html

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Tags : Project Euler Problem 9 solution in Java, Mathematics problems, Special Pythagorean Triplet, for loop, if else statement.