# Project Euler: Problem 9

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.

I first created two lists, A and B, and set them to all values up to 1000.

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In [50]:

A = range(1000)
B = range(1000)

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Using two for loops, I looped through all the values in A, then all the values in B. Using the formulas for pythagorean triples from the wikipedia page about them, I used an if statement that said if the value in B was larger than the value in A, then to define three variables by their respective formula. These would be my pythagorean triples. Finally, I created another if statement that compared whether the sum of the pythagorean triples was 1000. If the sum was 1000, I printed the product.

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In [51]:

for n in A:
for m in B:
if m > n:
a = m ** 2 - n ** 2
b = 2 * m * n
c = m ** 2 + n ** 2
if a + b + c == 1000:
print(a * b * c)

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31875000

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In [ ]:

# This cell will be used for grading, leave it at the end of the notebook.

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