Bezout's Theorem Suppose that \(a\) and \(b\) are integers that are not both zero. There exists integers \(x\) and \(y\) so that $$ax + by = \gcd(a,b).$$

In class, you were shown how to compute these using back substitution in Euclid's algorithm. You will now implement this algorithm in Python. Shell code is provided here. Note that these integers can be negative. Test all corners!

def bezout(a, b):
    """precondition: a and b are integers, not both zero.
postcondition:  return a tuple (x,y) so that a*x + b*y = gcd(a,b)."""
    pass

def main():
    print("Testing the bezout function")
    pass
main()