Project Euler

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# [[Problem 9]]

## Special Pythagorean Triplet

A Pythagorean triplet is a set of three natural numbers, $a \lt b \lt c$, for which,

$$a^2 + b^2 = c^2.$$

For example, $3^2 + 4^2 = 9 + 16 = 25 = 5^2$.

There exists exactly one Pythagorean triplet for which $a + b + c = 1000$.

Find the product $abc$.

## 特別なピタゴラス数

ピタゴラス数(ピタゴラスの定理を満たす自然数)とは a < b < c で以下の式を満たす数の組である.

$$a^2 + b^2 = c^2.$$

例えば, $3^2 + 4^2 = 9 + 16 = 25 = 5^2$ である.

a + b + c = 1000 となるピタゴラスの三つ組が一つだけ存在する.

これらの積 abc を計算しなさい.

```scheme

#!r6rs

#!chezscheme

(import (chezscheme))

(define sum-1000-triplets

  (let loop1 ([a 1] [result '()])

    (if (< 333 a)

      result

      (let loop2 ([b a] [result result])

        (if (< 499 b)

          (loop1 (add1 a) result)

          (let ([c (- 1000 a b)])

            (loop2 (add1 b) (cons `(,a ,b ,c) result))))))))

(define (pythagorean? a b c)

  (= (+ (expt a 2) (expt b 2))

     (expt c 2)))

(define pythagorean-triplets

  (filter

    (lambda (lis)

      (apply pythagorean? lis))

    sum-1000-triplets))

(assert (= (length pythagorean-triplets) 1))

(define answer-9

  (apply * (car pythagorean-triplets)))

(printf "9: ~D~%" answer-9)

```