Number Theory
Explore divisibility and congruences; arithmetic functions and equations; prime distribution and advanced connections. Concepts and connections are available independently of video coverage.
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Quadratic residues
A residue is quadratic when it is congruent to a square modulo the chosen integer.
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Diophantine equations
Diophantine equations seek integer or rational solutions rather than unrestricted real solutions.
Euler's totient
Euler's totient counts positive residues coprime to a positive integer modulus.
Modular arithmetic
Congruence identifies integers with the same remainder modulo a positive integer.
Algebraic numbers
An algebraic number is a root of a nonzero polynomial with rational coefficients.
Finite fields
A finite field has prime-power size; fields of each such size exist and are unique up to isomorphism.
Knowledge connections
- Diophantine equations · Related · Map context
- Euler's totient · Related · Map context
- Modular arithmetic · Prerequisite · Map context