#lang sicp
(define (square x) (* x x))
(define (expmod-aux base exp n acc)
  (cond ((= 0 exp) acc)
        ((even? exp) (expmod-aux (remainder (square base) n) (/ exp 2) n acc))
        (else (expmod-aux base (- exp 1) n (remainder (* acc base) n)))))
(define (expmod base exp n)
  (expmod-aux base exp n 1))
(define (carmichael-test-aux n a)
  (cond ((>= a n) #t)
        ((= (expmod a n n) a) (carmichael-test-aux n (+ a 1)))
        (else #f)))
(define (carmichael-test n)
  (carmichael-test-aux n 0))
;> (carmichael-test 561)
;#t
;> (carmichael-test 1105)
;#t
;> (carmichael-test 1729)
;#t
;> (carmichael-test 2465)
;#t
;> (carmichael-test 2821)
;#t
;> (carmichael-test 6601)
;#t
;>