(*
The 5-digit number, 16807=7^(5), is also a fifth power. Similarly, the 9-digit number, 134217728=8^(9), is a ninth power.

How many n-digit positive integers exist which are also an nth power?
*)


open Big_int;;

let digits x =
  let rec digits b =
    if (gt_big_int b x) then 0 else (1+(digits (mult_int_big_int 10 b)))
  in
    digits (big_int_of_int 1)
;;

let search =
  let rec search x y n =
    if(x > 9) then n else
    let e = power_int_positive_int x y in
    let d = digits e in
    if(d < y) then search (x+1) 1 n else
    if(d > y) then search x (y+1) n else
    ( Printf.printf "%d %d %s %d\n" x y (string_of_big_int e) d;
      search x (y+1) (n+1) )
  in
    search 1 1 0
;;

Printf.printf "%d\n" search;;