Category:Number Theory

A

• [+] Algebraic Number Theory‎ (2)
• [+] Analytic Number Theory‎ (1)
• [+] Arithmetic‎ (3)

B

• [×] Binomial Coefficients‎ (0)

C

• [×] Class Field Theory‎ (0)
• [×] Computational Number Theory‎ (0)
• [×] Continued Fractions‎ (0)
• [×] Coprime‎ (0)

D

• [×] Diophantine Equations‎ (0)
• [×] Divisibility‎ (0)
• [×] Divisibility Tests‎ (0)

E

• [×] Euclid Book IX‎ (0)

F

• [×] Factorials‎ (0)
• [×] Fibonacci Numbers‎ (0)
• [+] Figurate Numbers‎ (1)
• [×] Floor and Ceiling‎ (0)

G

• [×] Generating Functions‎ (0)
• [×] Greatest Common Divisor‎ (0)

I

• [×] Interesting Numbers‎ (0)
• [×] Irrationality Proofs‎ (0)

K

• [×] Kummer Theory‎ (0)

L

• [×] Lowest Common Multiple‎ (0)

M

• [×] Modulo Arithmetic‎ (0)
• [×] Multiplicative Functions‎ (0)

N

• [×] Number Bases‎ (0)
• [+] Numbers‎ (9)

P

• [×] Prime Numbers‎ (0)
• [×] Pythagorean Triples‎ (0)

Q

• [×] Quadratic Residues‎ (0)

S

• [×] Square Numbers‎ (0)
• [×] Sums of Sequences‎ (0)
• [×] Sums of Squares‎ (0)
• [×] Superfunctions‎ (0)

T

• [×] Transcendental Number Theory‎ (0)
• [×] Triangular Numbers‎ (0)

0

• 0.999...=1

1

• 1+2+...+n+(n-1)+...+1 = n^2

A

• Absolute Value Bounded Below by Zero

B

• Backwards Induction
• Bézout's Lemma

C

• Chen's Theorem
• Congruence of Sum of Digits to Base Less 1

D

• Division Theorem
• Divisor of Sum of Coprime Integers

E

• Equivalence of Definitions of the Second Chebyshev Function
• Euclid's Lemma
• Euclid's Lemma for Prime Divisors
• Euclidean Algorithm
• Euler Phi Function Even for Argument Greater than 2
• Euler Phi Function of a Prime
• Euler Phi Function of an Integer
• Euler Phi Function of Product with Prime
• Euler's Criterion
• Euler's Theorem
• Even Perfect Numbers are Triangular
• Exact Form of Prime-Counting Function

F

• Factors of Mersenne Numbers
• Fermat's Last Theorem
• Fermat's Little Theorem
• Finitely Many Reduced Associated Quadratic Irrationals
• First Supplement to the Law of Quadratic Reciprocity

G

• Gauss's Lemma (Number Theory)
• Goldbach Conjecture implies Weak Goldbach Conjecture

G cont.

• Goldbach implies Bertrand

I

• Integer Absolute Value Greater than Divisors
• Integer Combinations Multiples of GCD
• Integer to Power of Multiple of Order
• Integers Bounded Above has Maximal Element
• Integers Bounded Below has Minimal Element
• Integers with Primitive Roots
• Integral Multiple of an Algebraic Number

L

• Law of Quadratic Reciprocity
• Locker Problem
• Lucas' Theorem
• Lucas-Lehmer Test

O

• Odd Integer 2n + 1
• Order Modulo n of Power of Integer
• Order of the Divisor Function
• Order of the Moebius Function

P

• Power of Sum Mod Prime
• Prime Power of Sum Modulo Prime
• Primitive Root is Generator of Reduced Residue System
• Principle of Complete Induction
• Principle of Mathematical Induction
• Principle of Strong Induction
• Product of Sigma and Euler Phi Functions
• Products of Sums
• Properties of Legendre Symbol
• Pólya-Vinogradov Inequality

Q

• Quadratic Nature by Sum of Floors of Multiples of Fractions
• Quotient and Remainder to Number Base

R

• Rational Square Root of Integer is Integer

S

• Second Principle of Finite Induction
• Second Principle of Mathematical Induction
• Second Supplement to the Law of Quadratic Reciprocity
• Set of Divisors of an Integer
• Sigma of an Integer
• Sigma of Power of Prime
• Sigma of Prime Number
• Square Root of 2 Is Irrational
• Sum of Euler Phi Function over Divisors
• Sum of Even Integers is Even
• Sum of Moebius Function over Divisors
• Sum of Odd Positive Powers
• Sum of Reciprocals of Divisors equals Abundancy
• Sum of Reciprocals of Primes is Divergent
• Sum Over Divisors Equals Sum Over Quotients

T

• Tau Function - Number of Positive Divisors
• Tau Function Odd Iff Argument is Square
• Tau Function of Square-Free Integer is Power of 2
• Tau of Power of Prime
• Theorem of Even Perfect Numbers
• There exist irrational a and b such that a^b is rational

U

• Upper Bounds for Prime Numbers

V

• Values of Legendre Symbol

W

• Waring's Problem
• Well-Ordering Principle