You are a holdover tenant in this instance, which by default means you have a month to month rental contract. A month to month residential rental agreement is terminated, after more than 30 days notice, on the last day of the next periodic term, i.e., the end of November here. So, giving notice at any time in October will be sufficient to terminate your month to month tenancey, and you will have to be out at the end of November.
You do not have to be out in three days.
The response by Mr. Ellingson is excellent advice. I just would like to add that we are assuming that the rent was paid monthly, and not for a shorter period of time, such as weekly. We are also assuming that the reason for the termination notice was not based on health violation reasons or failure to pay the rent.
It is also curious that the landlord had the neighbor deliver some letter to you which controverts what the landlord told you. I would suggest that you contact the landlord to discuss positions and try to reach a resolution before confusion leads down a path of action which would be more difficult to resolve.