Today’s problem in Project Euler, is related to probably THE most well known theorem of all times. Pythagoras theorem stating that

The square of the hypotenuse is the sum of squares of the two other sides.

It can also be stated in a more geometrical way as

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle

Which can also be shown in a graphical sense, on the figure to the right, where the blue area equals the orange area.

But enough with the background info, the problem reads

**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.**

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