p’ = p^{2} + q^{2}

q’ = 2pq + q^{2}

(define (fib n)
(fib-iter 1 0 0 1 n))
(define (fib-iter a b p q count)
(cond ((= count 0) b)
((even? count)
(fib-iter a
b
(+ (square p) (square q)) ; p'
(+ (* 2 p q) (square q)) ; q'
(/ count 2)))
(else (fib-iter (+ (* b q) (* a q) (* a p))
(+ (* b p) (* a q))
p
q
(- count 1)))))

It took me several attempts at getting the formula for p’ and q’ correct :(

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