The corporate powers of any corporation formed under this article shall be exercised by a board of not less than three directors who shall be stockholders of the company, and a majority of them citizens of the United States, and at least one-third of whom shall be residents of this state. Such directors shall be elected annually, after the expiration of the term of the directors named in the articles of incorporation, at such time and place, and upon such notice, and in such mode as the bylaws of the company may provide; but all such elections shall be by ballot, and each stockholder, either in person or by proxy, shall be entitled to as many votes as he owns shares of stock, and the persons receiving the greatest number of votes shall be declared elected. When a vacancy occurs in the office of director by death, resignation or otherwise, such vacancy shall be filled for the remainder of the year in such manner as the bylaws shall prescribe. Should there be no election of directors, on the day fixed in the bylaws for such election, such election may be held at such other time as the bylaws may designate, and the directors in office may continue to act until their successors are elected.