The method of nomination for all candidates for city elections shall be by petition. Not less than twenty-five (25) registered electors of the city shall sign such petitions for each candidate. No person shall sign his or her name to a greater number of petitions for any one office than there are persons to be elected to said office at the following regular or special city election. If a qualified and registered elector signs nominating petitions for a greater number of candidates than there are persons to be elected to said office, the signatures, if they bear the same date, shall not be counted upon any petition, and if they bear different dates, shall be counted in the order of their priority of date of filing for only so many candidates as there are persons to be elected. Nomination petitions shall be filed with the clerk up to 4:00 p.m., local time of the first Tuesday following the first Monday in August. The clerk shall publish notice of the last day permitted for filing nomination petitions and of the number of persons to be elected to each office at least one week and not more than three weeks before such last day.