A Pythagorean triplet is a set of three natural numbers, a b 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.

とりあえず単純に 

p009 = head [a*b*(1000-a-b)|a<-[1..1000],b<-[1..(a-1)],1000*(a+b)==500000+a*b]

↓をつかえばもっと高速化できるだろう。

http://ja.wikipedia.org/wiki/ピタゴラスの定理