Are you looking to obtain a patent or a copyright? They are not the same. Simply put a patent is for an invention while copyright is for an original work of authorship.
If you are trying to obtain a patent you will need to register it with the patent office. A copyright is with the copyright office (Part of the library of congress). You do not have to file for a copyright.
Copyright is to protect authorship of some type of work. This also includes audio and visual recordings. You can not copyright something such as an idea but you could copyright your expression of said idea. Same goes for something such as a math formula. Anything you create is autimaticly copyrighted in the United States. Though if you would prefer to better be protected you may file your work with the US copyright office. If you need to show the date of your creation then this would stand up in court better.
Patent is to protect something such as an invention. As stated by patent law what may be patented is “invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent”
You may not patent an idea.
There are three types of patents:
1) Utility patents may be granted to anyone who invents or discovers any new and useful process, machine, article of manufacture, or composition of matter, or any new and useful improvement thereof;
2) Design patents may be granted to anyone who invents a new, original, and ornamental design for an article of manufacture; and
3) Plant patents may be granted to anyone who invents or discovers and asexually reproduces any distinct and new variety of plant.
Hopefully that helps. Also trademark is not the same as the above two but the Patent Office does take care of that.