multiplicative inverse of modulo m in scheme

Question

I\'ve written the code for multiplicative inverse of modulo m. It works for most of the initial cases but not for some. The code is below:

(define (inverse x m)
         


        

Answer 1

Does it have to be precisely that algorithm? if not, try this one, taken from wikibooks:

(define (egcd a b)
  (if (zero? a)
      (values b 0 1)
      (let-values (((g y x) (egcd (modulo b a) a)))
        (values g (- x (* (quotient b a) y)) y))))

(define (modinv a m)
  (let-values (((g x y) (egcd a m)))
    (if (not (= g 1))
        #f
        (modulo x m))))

It works as expected:

(modinv 5 11) ; 9
(modinv 9 11) ; 5
(modinv 7 11) ; 8
(modinv 8 12) ; #f 
(modinv 5 12) ; 5