Editing Number Theory (section)

== <span style="color: #FFFFFF;">Remembering</span> ==
* '''Integer''' — A whole number: ..., −3, −2, −1, 0, 1, 2, 3, ... The central objects of number theory.
* '''Divisibility''' — a divides b (written a | b) if there exists an integer k such that b = ak.
* '''Prime number''' — An integer p > 1 whose only positive divisors are 1 and p itself.
* '''Composite number''' — An integer > 1 that is not prime; has at least one factor other than 1 and itself.
* '''Fundamental Theorem of Arithmetic''' — Every integer > 1 has a unique factorization into prime numbers.
* '''Greatest Common Divisor (GCD)''' — The largest positive integer dividing both a and b; computed by the Euclidean algorithm.
* '''Euclidean Algorithm''' — An ancient algorithm computing GCD(a,b) by repeated division: GCD(a,b) = GCD(b, a mod b).
* '''Modular arithmetic''' — Arithmetic "clock arithmetic"; a ≡ b (mod n) means n | (a − b).
* '''Congruence''' — a ≡ b (mod n): a and b leave the same remainder when divided by n.
* '''Fermat's Little Theorem''' — If p is prime and p ∤ a, then a^(p−1) ≡ 1 (mod p); foundation of RSA.
* '''Euler's Theorem''' — Generalization: a^φ(n) ≡ 1 (mod n) when gcd(a,n)=1; φ is Euler's totient function.
* '''Diophantine equation''' — A polynomial equation where only integer solutions are sought.
* '''Fermat's Last Theorem''' — No integer solutions to x^n + y^n = z^n for n > 2; proved by Wiles 1995.
* '''Goldbach's Conjecture''' — Every even integer > 2 is the sum of two primes; unproven since 1742.
* '''Riemann Hypothesis''' — All non-trivial zeros of the Riemann zeta function have real part 1/2; most important unsolved problem in mathematics.
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