Exercise 2.5: Show that we can represent pairs of nonnegative integers using only numbers and
arithmetic operations if we represent the pair
b as the integer that is the product
2a 3b. Give the corresponding definitions of the procedures
The discrete log procedure is a cousin of
discrete-log from 1.45.
(define (cons a b) (* (expt 2 a) (expt 3 b))) (define (car x) (discrete-log x 2)) (define (cdr x) (discrete-log x 3)) (define (discrete-log n base) (if (not (= 0 (remainder n base))) 0 (+ 1 (discrete-log (/ n base) base))))