Project Euler 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, 32 + 42 = 9 + 16 = 25 = 52.

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

Find the product abc.

Solution: The problem involves finding a triplet which meets two conditions

a

^{2}+ b^{2}= c^{2}

and

a + b + c = 1000.

We do this by finding c value by getting square root of a^{2} + b^{2}. Now for the a,b and c value we check if a + b + c = 1000. If this condition is met, we find the product of a,b and c. This is the solution of our problem.

**Java Program to find the only Pythagorean triplet, {a, b, c}.**

`public`

`class`

FindPythagoreonTriplet `{`

` ``public`

`static`

`int`

findPythagonTriplet`(`

`)`

`{`

` ``int`

k=0;

` `

` ``for`

`(`

`int`

i=1;i<1000;i++`)`

`{`

` ``for`

`(`

`int`

j=i+1;j<999;j++`)`

`{`

` k = ``(`

`int`

`)`

Math.sqrt`(`

i*i + j*j`)`

;

` `

` ``if`

`(`

i+j+k==1000 && i<j && j<k`)`

`{`

` ``if`

`(`

i*i+j*j==k*k`)`

` ``return`

i*j*k;

` ``}`

` ``}`

` ``}`

` `

` ``return`

0;

` ``}`

` `

` ``public`

`static`

`void`

main`(`

String `[`

`]`

args`)`

`{`

` System.out.print``(`

findPythagonTriplet`(`

`)`

`)`

;

` ``}`

`}`

Happy Coding !!!