---
title: "AFM.NR.4: Number Theory Applications (Georgia Mathematics standard)"
code: AFM.NR.4
cite_as: Georgia Standards of Excellence, Mathematics, AFM.NR.4
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/AFM.NR.4
md_url: https://georgiahomeroom.org/standards/code/AFM.NR.4.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/AFM.NR.4.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# AFM.NR.4: Number Theory Applications

Apply number theory and number-theoretic operations to solve contextual, mathematical problems and to explain real-life phenomena.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- Use number-theoretic operations.
  - **AFM.NR.4.1**: Apply the divides relation to positive integers and calculate one integer modulo another integer.
  - **AFM.NR.4.2**: Find the inverse of an integer for a certain modulus.
  - **AFM.NR.4.3**: Calculate the floor and the ceiling of a real number.
- Prove statements in number theory.
  - **AFM.NR.4.4**: Prove statements involving properties of numbers.
  - **AFM.NR.4.5**: Prove statements involving the floor and ceiling functions.
  - **AFM.NR.4.6**: Prove the Fundamental Theorem of Arithmetic, the Euclidean algorithm, and Fermat’s Little Theorem.

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.