# Project Euler 48

In order to keep the numbers in check we use the rule that

$$ a \equiv v (\bmod m) \Rightarrow a b \equiv v b (\bmod m) $$

This rule is implemented in the powermod function. Note, that the powermod function is not yet “tail recursive” and is therefore vulnerable to stack overflow for (very) large b.

#light let rec powermod a b m = if b = 0I then 1I else (a*(powermod a (b-1I) m)) % m let sum = let numbers = [1I .. 1000I] let res = Seq.zip numbers numbers |> Seq.map (fun (a,b) -> powermod a b 10000000000I) |> Seq.sum res % 10000000000I printfn "%A" sum System.Console.ReadLine() |> ignore