075.py

"""
Project Euler Problem 75
========================

It turns out that 12 cm is the smallest length of wire can be bent to form
a right angle triangle in exactly one way, but there are many more
examples.

12 cm: (3,4,5)
24 cm: (6,8,10)
30 cm: (5,12,13)
36 cm: (9,12,15)
40 cm: (8,15,17)
48 cm: (12,16,20)

In contrast, some lengths of wire, like 20 cm, cannot be bent to form a
right angle triangle, and other lengths allow more than one solution to be
found; for example, using 120 cm it is possible to form exactly three
different right angle triangles.

120 cm: (30,40,50), (20,48,52), (24,45,51)

Given that L is the length of the wire, for how many values of L 2,000,000
can exactly one right angle triangle be formed?
"""
from math import ceil, gcd

max_num = 1500000
instances = [0 for _ in range(1500000)]
singles = 0

for m in range(1, 866):
    for n in range(1, m):
        for k in range(1, ceil(max_num / (2 * m * (m + n)))):
            if not (m % 2 == n % 2) and gcd(m, n) == 1:
                potential_sum = 2 * k * m * (m + n)
                # print(k, m, n)
                instances[potential_sum] += 1
                if instances[potential_sum] == 1:
                    singles += 1
                if instances[potential_sum] == 2:
                    singles -= 1

print(singles)