> For the complete documentation index, see [llms.txt](https://hub.bsvblockchain.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://hub.bsvblockchain.org/wiki/cryptography-and-keys/cryptography/modular-arithmetic.md). # Modular arithmetic Modular Arithmetic is a system of arithmetic for integers, which considers the remainder. In modular arithmetic, numbers "wrap around" upon reaching a given fixed quantity (this given quantity is known as the modulus) to leave a remainder. It can be though of as a clock face with the modulus amount of numbers on it. The modulus of n will be the value that you find if you wrapped around the clock values n times. --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation by asking a question. Perform an HTTP GET request on the following URL with the `ask` and `goal` query parameters: ``` GET https://hub.bsvblockchain.org/wiki/cryptography-and-keys/cryptography/modular-arithmetic.md?ask=&goal= ``` `ask` is the immediate question: it should be specific, self-contained, and written in natural language. `goal` is what the user is ultimately trying to achieve, the reason they need the answer. Sharing it helps GitBook give you a better, more relevant answer. A goal is most helpful when it describes the outcome the user wants rather than restating the question. For example, with `ask=how do I create an API token`, a goal like `automate deployments from our CI pipeline` lets GitBook tailor the answer to that use case. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.