"""

A little mathematical challenge. Consider right-angle triangles with side lengths a, b and c ,
where a is the shortest side and c the longest. Write a Python script to find all possible side lengths,
where all three side lengths are integers. Don't include multiples of already found solutions.,
for example, your result should show 3, 4, 5 but not 6, 8, 10. Compute for all integer lengths of a from 1 to 1000.

For clarification, let's say that none of the sides can be longer than 1000.
Rather than print all the combinations, tell us how many triangles you find.
I would like to see solutions that don't import any libraries.

"""

def searchForMultiples(_a,_b,_c,_triangles):
    if len(_triangles) == 0:
        return [[_a,_b,_c]] , False
    for t in _triangles:
        if _a % t[0] == 0:
            divisor = _a / t[0]
            if _b % t[1] == 0 and _b / t[1] == divisor:
                if _c % t[2] == 0 and _c / t[2] == divisor:
                    return _triangles, True

    _triangles.append([_a,_b,_c])
    print(_a, _b, _c)
    return _triangles , False

def mainV1():
    triangles = []
    for a in range(1, 1001):
        for b in range(a, 1001):
            c = (a**2 + b**2)**0.5
            if c.is_integer() and c <= 1000:
                c = int(c)
                triangles , checkForMultiples = searchForMultiples(a, b, c, triangles)

    print(f"Number of right-angle triangles found: {len(triangles)}")
    return triangles

mainV1()