Exercise 1.3

Proof. With direct instructions in Python, we obtain :

>>> a, b = 187,  221
>>> print("q = ",a//b); a, b = b, a%b; print(a,b)
q =  0
221 187
>>> print("q = ",a // b); a, b = b, a%b; print(a,b)
q =  1
187 34
>>> print("q = ",a // b); a, b = b, a%b; print(a,b)
q =  5
34 17
>>> print("q = ",a // b); a,b = b, a%b; print(a,b)
q =  2
17 0

This gives the equalities

So $187\wedge 221=17$.

With the same instructions, we obtain

$6188\wedge 4709=17$.

Finally

$314\wedge 159=1$.

The Python script which gives the gcd is very concise :

def gcd(a,b):
    a, b = abs(a), abs(b)
    while b != 0:
        a, b = b, a % b
    return a

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