---
title: "Number Theory"
description: "8 topics in Mathematics, in the order they build on each other."
canonical: https://lightmysky.com/learn/mathematics/areas/number-theory
source: https://lightmysky.com/learn/mathematics/areas/number-theory.md
retrieved: 2026-09-02
---

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# Number Theory

8 topics in Mathematics, in the order they build on each other.

Page: https://lightmysky.com/learn/mathematics/areas/number-theory

- [Divisibility and the Division Algorithm](https://lightmysky.com/learn/mathematics/divisibility-and-the-division-algorithm-mt_UkQNs-6-40): Fix what divides means, prove that division leaves a unique quotient and remainder, and use that uniqueness as the base of everything after it.
- [Euclid's Algorithm and Bezout's Identity](https://lightmysky.com/learn/mathematics/euclids-algorithm-and-bezouts-identity-mt_26hM0EnJpq): Find a greatest common divisor by repeated division instead of by factorising, then run the algorithm backwards to write it as a combination of the two numbers.
- [Modular Arithmetic and Congruence Classes](https://lightmysky.com/learn/mathematics/modular-arithmetic-and-congruence-classes-mt_Lt4_Aazx2j): Agree to identify integers with the same remainder, check the arithmetic survives that identification, and compute in the resulting finite system.
- [Linear Congruences and the Chinese Remainder Theorem](https://lightmysky.com/learn/mathematics/linear-congruences-and-the-chinese-remainder-theorem-mt_J9_RMpwcRX): Solve a single linear congruence, say exactly when it is solvable, and combine congruences with coprime moduli into one.
- [Fermat's Little Theorem and Euler's Theorem](https://lightmysky.com/learn/mathematics/fermats-little-theorem-and-eulers-theorem-mt_7wW4z4Eidx): Prove that raising a unit to the size of the unit group returns one, and use it to shortcut enormous modular powers.
- [Primitive Roots and the Units Modulo n](https://lightmysky.com/learn/mathematics/primitive-roots-and-the-units-modulo-n-mt_KwTDckkMze): Ask when the units modulo n are generated by a single element, and settle which n admit one.
- [Quadratic Residues and the Law of Reciprocity](https://lightmysky.com/learn/mathematics/quadratic-residues-and-the-law-of-reciprocity-mt_0KS9eTCY4p): Decide which residues are squares modulo a prime, compute the Legendre symbol, and use reciprocity to answer the question quickly.
- [The Distribution of Primes and What Is Still Open](https://lightmysky.com/learn/mathematics/the-distribution-of-primes-and-what-is-still-open-mt_PJwm9kuQWQ): Prove the primes never run out, meet the estimate for how thinly they spread, and see where the honest boundary of current knowledge sits.