I have a question regarding a problem that is done in DrRack

I have a question regarding a problem that is done in DrRacket.

Question 1: The famous computer scientist, Edsger Dijkstra, made the following observations for m and n >= 1:

1. If m = n, then the greatest common divisor of m and n is m.

2. If m > n, then the greatest common divisor of m and n is the greatest divisor of m-n and n.

Based on these observations, implement a function to compute the greatest common divisor of two given numbers >= 1. Follow all the steps of the design recipe. and write the termination argument.

Below is what I have so far. But i\'m sure its wrong recording the questions above. can someone help please?

;1. If m = n, then the greatest common divisor of m and n is m.
;2. If m > n, then the greatest common divisor of m and n is
;   the greatest divisor of m-n and n.
(define (greatest-common-divisor n m)
(local [(define (first-divisor-<= i)
            (cond [(=i 1) 1]
                  [else (cond [(and (= (remainder n i) 0)
                                    (= (remainder m i) 0))
                               i]
                              [else (first-divisor-<= (sub1 i))])]))]
    (first-divisor-<= (min m n))))

;Termination Argument
;There are 2 positive numbers in and that is the largest integers
;When returning m n, assuming one of them is 0 but actually returning non zero

(check-expect (greatest-common-divisor 0) 0)
(check-expect (greatest-common-divisor 6 12 8) 2)

Solution

So, following is the recursive function to calculate the GCD of two numbers based on the observations of Edsger Dijkstra.

Python code:

def gcd(n,m):
   if(n ==m):
       return n
   elif(n > m):
       return gcd(n-m, m)
   else:
       return gcd(n,m-n)

Sample Output:

20
1
29