#lang racket
; Returns the result of raising base to the (non-negative) power exp.
(define (pow base exp)
  (if (< exp 1)
      1
      (* base (pow base (- exp 1)))))
  
  
; Returns n!.
(define (factorial n)
  (if (<= n 1)
      1
      (* n (factorial (- n 1)))))
  
; Returns the nth number in the Fibonacci series (0-indexed).
(define (fib n)
  (if (<= n 1)
      1
      (+ (fib (- n 1)) (fib (- n 2)))))

; Returns #t if n is prime and #f otherwise.
; The first function shown is a helper function.
; This is not a fancy solution (such as the sieve of Eratosthenes)
; just a naive solution that checks if n is divisible by any
; integer in the range [2,n-1].
(define (prime?-help candidate divisor)
  (or (>= divisor candidate) ; divisor is at least candidate
      (and (not (= 0 (modulo candidate divisor))) ; candidate is not divisible by divisor
           (prime?-help candidate (+ divisor 1)))))
(define (prime? n) (and (>= n 2) (prime?-help n 2)))