# this file available at: https://arachnoid.com/files/python01/
import math

# pythagorean triple:
# https://mathworld.wolfram.com/PythagoreanTriple.html
# https://en.wikipedia.org/wiki/Pythagorean_triple

def gcd(a:float,b:float) -> float:
    if b == 0:
        return a
    else:
        return gcd(b, a%b)
    
def triple_search(max : int = 100) -> int:
    width = 4
    count = 0
    print(f'{"a":>{width}} {"b":>{width}} {"c":>{width}}')
    print('------------------')
    for a in range(1,max+1):
        for b in range(a,max+1):
            c = (a*a+b*b)**0.5
            ic = int(c)
            # if gcd of a,b,c = 1 and c is an integer
            if c == ic and math.gcd(a,math.gcd(b,ic)) == 1:
                count += 1
                print(f'{a:{width}} {b:{width}} {ic:{width}}')
    return count

def main():
    max = 100
    count = triple_search(max)
    print(f'\nResult: {count} primitive Pythagorean triples with a,b side lengths <= {max}')

if __name__ == "__main__":
    main()