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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Prime number theorem
The number of primes up to x is asymptotic to x divided by log x.
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Euler's totient
Euler's totient counts positive residues coprime to a positive integer modulus.
Fields
A field is a commutative ring where every nonzero element has a multiplicative inverse.
Finite fields
A finite field has prime-power size; fields of each such size exist and are unique up to isomorphism.
Riemann zeta function
A Dirichlet series over positive integers defines zeta in a convergent half-plane and admits analytic continuation.
Algebraic numbers
An algebraic number is a root of a nonzero polynomial with rational coefficients.
Knowledge connections
- Riemann zeta function · Related · Map context
- Finite fields · Related · Map context
- Euler's totient · Related · Map context
- Fields · Related · Map context