Category:Number Theory
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This category contains results about Number Theory.
Definitions specific to this category can be found in Definitions/Number Theory.
Number theory is the branch of mathematics which studies the properties of the integers, and by extension the rational numbers and related number systems.
Subcategories
This category has the following 200 subcategories, out of 268 total.
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- 0.999...=1 (6 P)
A
- Additive Arithmetic Functions (empty)
- Aliquot Sums (2 P)
- Amicable Triplets (4 P)
- Aurifeuillian Factorizations (3 P)
- Axiom of Archimedes (8 P)
B
- Beatty Sequences (10 P)
- Bernoulli Polynomials (3 P)
- Bertrand-Chebyshev Theorem (8 P)
- Bézout's Identity (12 P)
C
- Cantor Pairing Function (4 P)
- Catalan's Conjecture (3 P)
- Class Field Theory (empty)
- Collatz Conjecture (9 P)
- Common Divisors (empty)
- Computational Number Theory (empty)
- Continued Square Roots (empty)
- Cyclic Numbers (1 P)
D
- Digital Roots (6 P)
- Diophantine m-Tuples (2 P)
- Dirichlet Convolution (8 P)
- Dismal Arithmetic (empty)
- Division Theorem (29 P)
- Double Factorials (1 P)
E
F
- Fermat Quotients (2 P)
- Fermat's Last Theorem (3 P)
- Fermat's Little Theorem (22 P)
- Fleenor-Heronian Triangles (1 P)
- Forward-Backward Induction (2 P)
G
- Goldbach Conjecture (6 P)
H
- Harmonic Sequences (1 P)
- Hensel's Lemma (14 P)
- Hilbert-Waring Theorem (33 P)
- Hyperoperation (5 P)
I
- Integer Sequences (2 P)
- Integral Ideals (4 P)
- Interesting Numbers (empty)
K
- Kronecker Delta (empty)
- Kummer Theory (empty)
L
- Locker Problem (3 P)
M
- Mills' Theorem (4 P)
N
- Number Sieves (1 P)
O
- Oesterlé-Masser Conjecture (6 P)
P
- Pandigital Fractions (27 P)
- Peano Arithmetic (empty)
- Pell Numbers (7 P)
- Penholodigital Integers (11 P)
- Prime Gaps (11 P)
- Prime Triplets (1 P)
- Primitive Prime Factors (1 P)
- Product of Proper Divisors (1 P)
- Pseudoprimes (Number Theory) (empty)
Q
- Quadratic Irrationals (4 P)
- Quasiperfect Numbers (3 P)
R
Pages in category "Number Theory"
The following 181 pages are in this category, out of 181 total.
1
A
C
- Casting Out Nines
- Catalan's Conjecture
- Characteristic Function of Square-Free Integers is Multiplicative
- Chen's Theorem
- Chinese Remainder Theorem
- Collatz Conjecture
- Commensurability is Transitive
- Completely Additive Function is Additive
- Completely Multiplicative Function is Multiplicative
- Conditions for Integer to have Primitive Root
- Congruence of Sum of Digits to Base Less 1
- Constant to Power of Number of Distinct Prime Divisors is Multiplicative Function
- Definition:Continued Square Root
- Continuum Property implies Well-Ordering Principle
- Coprimality Criterion
- Cube Root of 2 is Irrational
- Cyclic Permutations of 5-Digit Multiples of 41
D
E
- Eisenstein Integers form Integral Domain
- Eisenstein's Lemma
- Equality of Integers to the Power of Each Other
- Equivalence of Definitions of Second Chebyshev Function
- Euclidean Algorithm
- Euler's Criterion
- Euler's Pentagonal Numbers Theorem
- Euler's Sum of Powers Conjecture
- Euler's Theorem (Number Theory)
- Exact Form of Prime-Counting Function
- Existence of Number to Power of Prime Minus 1 less 1 divisible by Prime Squared
- Existence of Prime-Free Sequence of Natural Numbers
- Existence of q for which j - qk is Positive
- Existence of Rational Powers of Irrational Numbers
F
G
H
I
- Infinite Number of Primes of form 4n - 1
- Integer as Sum of Seven Positive Cubes
- Integer as Sum of Three Odd Squares
- Integer Less One divides Power Less One
- Integer Less One divides Power Less One/Corollary
- Integer Less One divides Power Less One/Corollary/Converse
- Integer to Power of Multiple of Order
- Integer to Power of Multiple of Order/Corollary
- Integer to Power of p-1 over 2 Modulo p
- Integer to Rational Power is Irrational iff not Integer or Reciprocal
- Integers as Sum of Three Pairwise Coprime Integers
- Integers Representable as Product of both 3 and 4 Consecutive Integers
- Integral Multiple of an Algebraic Number
- Irrationality of Logarithm
L
- Lagrange's Theorem (Number Theory)
- Largest Mutually Coprime Subset of Initial Segment of Natural Numbers
- Largest Prime Factor of n squared plus 1
- Length of Reciprocal of Product of Powers of 2 and 5
- Lifting The Exponent Lemma
- Liouville Numbers are Irrational
- Liouville's Theorem (Number Theory)
- Liouville's Theorem (Number Theory)/Corollary
- Local Maxima of Number of Goldbach Decompositions
- Locker Problem
- Lucas' Theorem
- Lucas' Theorem/Corollary
N
- Natural Number is Divisor or Multiple of Divisor of Another
- Non-Zero Integer has Finite Number of Divisors
- Number of Bits for Decimal Integer
- Number of Digits in Number
- Number of Digits to Represent Integer in Given Number Base
- Number of Multiples less than Given Number
- Number of Partitions as Coefficient of Power Series
- Number Plus One divides Power Plus One iff Odd
- Numbers Divisible by Sum and Product of Digits
- Numbers Equal to Sum of Squares of Digits
- Numbers Not Expressible as Sum of no more than 5 Squares of Composite Numbers
- Numbers not Sum of Square and Prime
- Numbers whose Cyclic Permutations of 3-Digit Multiples are Multiples
O
P
- Positive Integer is Sum of Consecutive Positive Integers iff not Power of 2
- Positive Rational Number as Power of Number with Power of Itself
- Power Function is Completely Multiplicative/Integers
- Power of Sum Modulo Prime
- Power of Sum Modulo Prime/Corollary
- Prime Divisors of Cyclotomic Polynomials
- Prime Power of Sum Modulo Prime
- Prime Power of Sum Modulo Prime/Corollary
- Primes of form Power plus One
- Primitive Root is Generator of Reduced Residue System
- Principle of Mathematical Induction
- Product of Integers of form 4n 1
- Product of Sums
- Product of Sums/Corollary
- Product of Three Consecutive Integers is never Perfect Power
R
- Ramanujan's Continued Fraction of One
- Ramanujan's Infinite Nested Roots
- Ramaré's Theorem
- Rational Number as Power of Number with Itself
- Rational Square Root of Integer is Integer
- Real Logarithm is Completely Additive
- Recurring Parts of Multiples of One Thirteenth
- Recurring Parts of Multiples of Reciprocal of 53
- Richert's Theorem
- Riemann Hypothesis implies Odd Number is Sum of at most 5 Primes
- Riemann Zeta Function and Prime Counting Function
- User:Robkahn131/Sandbox
S
- Set of Divisors of Integer
- Set of Integers Bounded Above by Integer has Greatest Element
- Set of Integers Bounded Above has Greatest Element
- Set of Integers Bounded Below has Smallest Element
- Set of Successive Numbers contains Unique Multiple
- Sets of 4 Integers a, b, c, d for which Every Integer is in form ax^2 by^2 cz^2 du^2
- Signum Complement Function on Natural Numbers as Characteristic Function
- Signum Function on Integers is Extension of Signum on Natural Numbers
- Signum Function on Natural Numbers as Characteristic Function
- Smallest n for which 2^n-3 is Divisible by n
- Smallest Positive Integer not of form -4 mod 9 not representable as Sum of Three Cubes
- Square of Quadratic Gauss Sum
- Squares Ending in 5 Occurrences of 2-Digit Pattern
- Squares Ending in n Occurrences of m-Digit Pattern
- Squares Ending in n Occurrences of m-Digit Pattern/Example
- Structure of Recurring Decimal
- Sum of Odd Positive Powers
- Sum of Reciprocals of Divisors equals Abundancy Index
- Sum of Reciprocals of Primes is Divergent/Lemma
- Sum of two Fourth Powers cannot be Fourth Power
- Sum Over Divisors Equals Sum Over Quotients