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

a2 + b2 = c2

For example, 32 + 42 = 9 + 16 = 25 = 52.

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

Find the product abc.

static void Main(string[] args)

        {

            for (int i = 1; i < 1000; i++)

            {

                for (int j = 1; j < 1000; j++)

                {

                    for (int k = 1; k < 1000; k++)

                    {

                        if (i + j + k == 1000)

                        {

                            if (j * j + k * k == i * i)

                            {

                                int x = i * j * k;

                                Console.WriteLine(x);

                            }

                        }

                    }

                }

            }

        }

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