IN SCHEME PROGRAMMING LANGUAGE (RACKET)

(define +mod

(lambda (a b n)

(modulo (+ a b) n)

))

(define -mod

(lambda (a b n)

(modulo (- a b) n)

))

(define *mod

(lambda (a b n)

(modulo (* a b) n)

Write a procedure exptmod that computes a b (mod n) using repeated squaring. You should use the given modular arithmetic operations, particularly mod, in your solution. Do not use expt or slow-exptmod in your solution.

(define exptmod (lambda (a b n) YOUR-CODE-HERE))

Test your code for at least the following cases:

(exptmod 2 0 10) ; -> 1 (exptmod 2 3 10) ; -> 8 (exptmod 3 4 10) ; -> 1 (exptmod 2 15 100) ; -> 68 (exptmod -5 3 100) ; -> 75

(What I have so far is given below but it doesn't really work.)

(define exptmod

(lambda (a b n)

(cond ((= b 1) 1)

((= b 0) (*mod 1 1 n))

((even? b) (*mod (* a a) (exptmod a (/ b 2) n) n))

(else (*mod (exptmod (* a (- b 1) n) n)))))