defmodule Squares do
  @moduledoc """
  Calculate sum of squares, square of sum, difference between two sums from 1 to a given end number.
  """

  @doc """
  Calculate sum of squares from 1 to a given end number.
  """
  @spec sum_of_squares(pos_integer) :: pos_integer
  def sum_of_squares(number) do
    div(number * (number + 1) * (2 * number + 1), 6)
  end

  @doc """
  Calculate square of sum from 1 to a given end number.
  """
  @spec square_of_sum(pos_integer) :: pos_integer
  def square_of_sum(number) do
    div(number * (number + 1), 2) ** 2
  end

  @doc """
  Calculate difference between sum of squares and square of sum from 1 to a given end number.
  """
  @spec difference(pos_integer) :: pos_integer
  def difference(number) do
    abs(square_of_sum(number) - sum_of_squares(number))
  end
end