Problem 9 » 履歴 » リビジョン 3
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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)
```