https://projecteuler.net/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, $3^2 + 4^2 = 9 + 16 = 25 = 5^2$.

There exists exactly one Pythagorean triplet for which $a + b + c = 1000$. Find the product abc.

```
In [4]:
```import math
A = [i for i in range(1000)] # a, b could be any value 0-999
B = [i for i in range(1000)]
for a in A:
for b in B: # I solved both equations for "c" and set them equal to each other. Since a and b cannot equal 0 (since this is a triangle) and a<b<c there can only be one answer
if math.sqrt(a**2 + b**2) == 1000 - a - b and a != 0 and b != 0 and b>a:
print(a*b*(1000-a-b))

```
```

```
In [ ]:
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# This cell will be used for grading, leave it at the end of the notebook.
```