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 answer-9

  (let loop1 ([a 1])

    (if (< 333 a)

      (error "answer-9" "answer-9 was not found!")

      (let loop2 ([b a])

        (if (< 499 b)

          (loop1 (add1 a))

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

            (if (= (+ (expt a 2)

                      (expt b 2))

                   (expt c 2))

              (* a b c)

              (loop2 (add1 b)))))))))

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

```