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# Problem 9

## Special Pythagorean triplet

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 $abc$.

## 特殊毕达哥拉斯三元组

$$a^2+b^2=c^2$$