defmodule Test do
  alias Caustic.Format
  import Caustic.Utils
  import Enum
  @moduledoc false
  def start do
    m = 14
    
    elems = 0..(m - 1) |> filter(&(gcd(m, &1) == 1))
    totient = count elems
    
    table = elems |> map(fn a ->
      2..totient |> map(&pow_mod(a, &1, m))
    end)
    
    col_labels = 2..totient |> map(& "a^#{&1}")
    
    IO.puts("m = #{m}")
    IO.puts("φ(m) = #{totient}")
    Format.print_table(table, elems, col_labels)
    
    IO.puts("")
    
    table2 = elems |> map(fn a ->
      elems |> map(& mod(a * &1, m))
    end)
    Format.print_table(table2, elems, elems)
  end
  
  def mp1 do
    p = mersenne_prime 29
    p - p
  end
  
  def mp2 do
    e = 132049
    p = pow(2, e) - 1
    p - p
  end
  
  def find_solutions(n, x_max) do
    # find solutions for x >= 0
    # it will be mirrored
    0..x_max
    |> Enum.map(&{&1, sqrti(&1 * &1 - n)})
    |> Enum.filter(fn {_, y} -> y !== nil end)
    |> Enum.flat_map(fn {x, y} -> [{x, y}, {-x, y}, {x, -y}, {-x, -y}] end)
    |> uniq()
  end
end