A Pythagorean triplet is a set of three natural numbers, a b c, for which,
a2 + b2 = c2
For example, 32 + 42 = 9 + 16 = 25 = 52.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
- Enumerate from 1 to 1000. Create tuples of all sets (m, n) where m > n.
- Create Pythagorean triplets using Euclid’s formula from the tuples.
- Find the set where a + b + c = 1000.
- Find the product of this set.
let problem9 = let pythagorean_triplets(m:int, n:int) = let a = m*m-n*n let b = 2*m*n let c = m*m+n*n [a;b;c] let tops = 1000 [for m in [1..tops] do for n in [1..m-1] do yield (m, n)] |> Seq.map (fun t -> pythagorean_triplets((fst t, snd t))) |> Seq.filter (fun x -> x |> Seq.sum = tops) |> Seq.head |> Seq.fold (fun acc elem -> acc * elem) 1
Download the source code with unit tests.