math utils

math_util.py

def gcd(a, b):
    """Return greatest common divisor using Euclid's Algorithm."""
    while b:
        a, b = b, a % b
    return a


def lcm(a, b):
    """Return lowest common multiple."""
    return a * b // gcd(a, b)


def egcd(a, b):
    """Return x and y such that
    ax + by = gcd(a, b)"""
    x, y, u, v = 0, 1, 1, 0
    while a != 0:
        q, r = b // a, b % a
        m, n = x - u * q, y - v * q
        b, a, x, y, u, v = a, r, u, v, m, n
    return b, x, y