Задание 1:

(define mdig (lambda (x)
               (if (< x 10)
                   x
                   (if (< (remainder x 10) (mdig (quotient x 10))) (remainder x 10) (mdig (quotient x 10))) ))

  )

Задание 2:

(define (eqdig x)
(define eqdig_raw (lambda (x)
                (if (< x 10)
                    x
                    (if (eq? (remainder x 10) (eqdig_raw (quotient x 10))) (remainder x 10) #f)  )))

  (if (eq? (eqdig_raw x) #f) #f #t)
  )

Задание 3:

(define (fact? max)
  (define fact (lambda (n x max)
                 (if (= max x)
                     (- n 1)
                     (if (> x max) #f (fact (+ n 1) (* x n) max)))) )
  (fact 1 1 max)
  )


Задание 4:

(define (findFib x)
  (define (find x a b c)
    (if (> (+ b c) x)
        (if (< (- x c) (- (+ b c) x)) c (+ b c)
            )
        (find x b c (+ c b)) )
    )
  (find x 1 1 2) )

Задание 5:

(define (perfect x)
  (define (temp x S d)
    (if (and (= S x) (= x d) )
        #t
        (if (= (remainder x d) 0)
            (temp x (+ S d) (+ d 1))
            (if (< d x)
                (temp x S (+ d 1))
                #f)
        )
    ))
  (temp x 0 1) )

(define (perfect x)
  (define (temp x del sum)
    (if (= x 1)
        #f
        (if (= x sum)
            #t
            (if (< (* del del) x)
                (if (= (remainder x del) 0)
                    (temp x (+ del 1) (+ sum del (/ x del)))
                    (temp x (+ del 1) sum)
                    )
                #f
                )
            )
        )
    )
  (temp x 2 1)
  )