Category:Number Theory

A

• [+] Algebraic Number Theory‎ (2 C, 12 P)
• [+] Analytic Number Theory‎ (1 C, 35 P)
• [+] Arithmetic‎ (3 C, 1 P)

B

• [×] Binomial Coefficients‎ (55 P)

C

• [×] Class Field Theory‎ (empty)
• [×] Computational Number Theory‎ (empty)
• [×] Continued Fractions‎ (16 P)
• [×] Coprime‎ (14 P)

D

• [×] Diophantine Equations‎ (5 P)
• [×] Divisibility‎ (48 P)
• [×] Divisibility Tests‎ (3 P)

E

• [×] Euclid Book IX‎ (2 P)
• [×] Euler Phi Function‎ (11 P)

F

• [×] Factorials‎ (6 P)
• [×] Fibonacci Numbers‎ (14 P)
• [+] Figurate Numbers‎ (1 C)
• [×] Floor and Ceiling‎ (22 P)

G

• [×] Generating Functions‎ (6 P)
• [×] Greatest Common Divisor‎ (28 P)

I

• [×] Interesting Numbers‎ (1 P)
• [×] Irrationality Proofs‎ (7 P)

K

• [×] Kummer Theory‎ (empty)

L

• [×] Lowest Common Multiple‎ (11 P)

M

• [×] Modulo Arithmetic‎ (84 P)
• [×] Moebius Function‎ (4 P)
• [×] Multiplicative Functions‎ (10 P)

N

• [×] Number Bases‎ (3 P)
• [+] Numbers‎ (9 C, 20 P)

P

• [×] Prime Numbers‎ (66 P)
• [×] Pythagorean Triples‎ (4 P)

Q

• [×] Quadratic Residues‎ (1 P)

S

• [×] Sigma Function‎ (6 P)
• [×] Square Numbers‎ (25 P)
• [×] Sums of Sequences‎ (39 P)
• [×] Sums of Squares‎ (10 P)
• [×] Superfunctions‎ (2 P)

T

• [×] Tau Function‎ (9 P)
• [×] Transcendental Number Theory‎ (8 P)
• [×] Triangular Numbers‎ (13 P)

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
• Bézout's Lemma/Proof 1
• Bézout's Lemma/Proof 2

C

• Chen's Theorem
• Collatz Conjecture
• Conditions on Existence of Order of Integer
• Congruence of Sum of Digits to Base Less 1

D

• Division Theorem
• Division Theorem/Proof 1
• Division Theorem/Proof 2
• Division Theorem/Proof 3
• Divisor of Sum of Coprime Integers
• Divisor Relation induces Lattice

E

• Eisenstein Integers form Integral Domain
• Equivalence of Definitions of the Second Chebyshev Function
• Euclid's Lemma
• Euclid's Lemma for Prime Divisors
• Euclid's Lemma for Prime Divisors/Corollary
• Euclid's Lemma for Prime Divisors/General Result
• Euclid's Lemma for Prime Divisors/General Result/Proof 1
• Euclid's Lemma for Prime Divisors/General Result/Proof 2
• Euclid's Lemma for Prime Divisors/Proof 1
• Euclid's Lemma for Prime Divisors/Proof 2
• Euclid's Lemma/Proof 1
• Euclid's Lemma/Proof 2
• Euclidean Algorithm
• Euler's Criterion
• Euler's Theorem
• Even Perfect Numbers are Triangular
• Exact Form of Prime-Counting Function
• Existence of Rational Powers of Irrational Numbers
• Existence of Rational Powers of Irrational Numbers/Proof 1
• Existence of Rational Powers of Irrational Numbers/Proof 2
• Existence of Rational Powers of Irrational Numbers/Proof 3

F

• Factors of Mersenne Numbers
• Fermat's Last Theorem
• Fermat's Little Theorem
• Fermat's Little Theorem/Corollary 1
• Fermat's Little Theorem/Corollary 1/Proof 1
• Fermat's Little Theorem/Corollary 1/Proof 2
• Fermat's Little Theorem/Corollary 2
• Fermat's Little Theorem/Proof 1
• Fermat's Little Theorem/Proof 2
• Fermat's Little Theorem/Proof 3
• 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
• Goldbach implies Bertrand
• Grimm's Conjecture

H

• Hilbert-Waring Theorem

I

• Integer Absolute Value Greater than Divisors
• Integer Absolute Value Greater than Divisors/Corollary
• Integer to Power of Multiple of Order
• Integers Bounded Above has Greatest Element
• Integers Bounded Above has Greatest Element/Proof 1
• Integers Bounded Above has Greatest Element/Proof 2
• Integers Bounded Below has Smallest Element
• Integers with Primitive Roots
• Integral Multiple of an Algebraic Number

L

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

M

• Minkowski's Theorem

N

• Norm of Eisenstein Integer

O

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

P

• Positive Rational Number as Power of Number with Power of Itself
• Power of Sum Mod Prime
• Power of Sum Mod Prime/Corollary

P cont.

• Prime Power of Sum Modulo Prime
• Prime Power of Sum Modulo Prime/Corollary
• Primitive Root is Generator of Reduced Residue System
• Principle of Complete Induction
• Principle of Mathematical Induction
• Principle of Strong Induction
• 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 Number as Power of Number with Itself
• 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
• Set of Integer Combinations equals Set of Multiples of GCD
• Signum Complement Function on Natural Numbers as Characteristic Function
• Signum Function on Integers as Extension
• Signum Function on Natural Numbers as Characteristic Function
• Square Root of 2 is Irrational
• Square Root of 2 is Irrational/Classic Proof
• Square Root of 2 is Irrational/Proof 2
• Square Root of 2 is Irrational/Proof 3
• Sum of Even Integers is Even
• 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

• Theorem of Even Perfect Numbers
• Third Principle of Mathematical Induction

U

• Upper Bounds for Prime Numbers

V

• Values of Legendre Symbol
• Vinogradov's Theorem/Corollary 1
• Vinogradov's Theorem/Corollary 2

W

• Waring's Problem
• Well-Ordering Principle