(define index1
  (lambda (n m)
    (define find-index
      (lambda (i)
        (if (= (remainder (expt n i) m) 1)
            i
            (find-index (+ i 1)))))
    (find-index 1)))


(define mod-expt
  (lambda (base exponent modulus)
    (define mod*
      (lambda (x y)
        (remainder (* x y) modulus)))
    (if (= exponent 0)
        1
        (mod* (mod-expt base (- exponent 1) modulus)
              base))))

(define index2
  (lambda (n m) 
    (define find-index
      (lambda (i)
        (if (= (mod-expt n i m) 1)
            i
            (find-index (+ i 1)))))
    (find-index 1)))