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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Euler's totient
Euler's totient counts positive residues coprime to a positive integer modulus.
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Fermat and Euler theorems
Coprime residues satisfy power congruences controlled by prime moduli or Euler's totient.
Prime factorization
Every integer greater than one factors uniquely into primes up to their order.
Prime number theorem
The number of primes up to x is asymptotic to x divided by log x.
Quadratic residues
A residue is quadratic when it is congruent to a square modulo the chosen integer.
Algebraic numbers
An algebraic number is a root of a nonzero polynomial with rational coefficients.
Knowledge connections
- Fermat and Euler theorems · Related · Map context
- Quadratic residues · Related · Map context
- Prime factorization · Related · Map context
- Prime number theorem · Related · Map context
- Prime factorization · Prerequisite · Map context