(define (expmod base exp m)
  (cond ((= exp 0) 1)
        ((even? exp)
         (remainder (square (expmod base (/ exp 2) m))
                    m))
        (else
         (remainder (* base (expmod base (- exp 1) m))
                    m))))

(define (test-carmichael n)
  (define (test a n)
    (= (expmod a n n) a))
  (define (go a n)
    (cond ((= a n) #t)
          ((test a n) (go (+ a 1) n))
          (else #f)))
  (go 1 n))