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 ≤ 1,500,000 can exactly one right angle triangle be formed?
In [1]:
from math import gcd
N = 1500000
s = int((N/2) ** 0.5)
count = [0]*N
for m in range(2, s):
for n in range(1 + (m%2), m, 2):
if gcd(m,n) > 1:
continue
L = 2*m*(m+n)
if L > N:
break
for k in range(L, N, L):
count[k] += 1
print(count.count(1))
In [ ]: