Editing Number Theory (section)

== <span style="color: #FFFFFF;">Creating</span> ==
Advanced research in number theory:
# '''Analytic number theory''': use complex analysis (Riemann zeta function) to study integer distribution.
# '''Algebraic number theory''': study rings of algebraic integers (Gaussian integers ℤ[i], cyclotomic fields) to prove results about ordinary integers.
# '''Arithmetic geometry''': elliptic curves, modular forms — the framework Wiles used.
# '''Computational number theory''': design and implement primality tests (AKS, Miller-Rabin), factoring algorithms (Pollard rho, quadratic sieve, general number field sieve), and their applications to cryptography.
# '''Additive combinatorics''': Green-Tao theorem (primes contain arbitrarily long arithmetic progressions) — synthesis of analytic and combinatorial methods.

[[Category:Mathematics]]
[[Category:Number Theory]]
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