If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.

{20,48,52}, {24,45,51}, {30,40,50}

For which value of p 1000, is the number of solutions maximised?

これはピタゴラス数の生成だ。 

import Data.List
import Data.Ord
pythagoras l = [2*k*m*(n+m)|n<-[1..l],m<-[(n+1)..(l`div`(n+1))],
k<-[1..(l`div`(2*m*(n+1)))],even m || even n,
gcd m n == 1 ,m>n,2*k*m*(n+m) < l]
count xs@(x:_)=(x,length xs)
p039 =fst.maximumBy(comparing snd).map count.group.sort.pythagoras