Fundamental theorem of arithmetic
GPTKB entity
Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
unique factorization theorem
|
| gptkbp:appliesTo |
positive integers
natural numbers greater than 1 |
| gptkbp:category |
elementary number theory
theorems in number theory |
| gptkbp:consequence |
factorization of integers is well-defined
structure of the integers as a unique factorization domain |
| gptkbp:dateOfFirstProof |
circa 300 BCE
|
| gptkbp:field |
number theory
|
| gptkbp:firstStatedIn |
gptkb:Euclid's_Elements
|
| https://www.w3.org/2000/01/rdf-schema#label |
Fundamental theorem of arithmetic
|
| gptkbp:implies |
prime numbers are the building blocks of integers
|
| gptkbp:provenBy |
gptkb:Euclid
|
| gptkbp:relatedTo |
gptkb:Prime_Number
algebraic number theory unique factorization domain prime factorization |
| gptkbp:state |
every integer greater than 1 is either a prime number or can be represented as a product of prime numbers
the prime factorization of an integer is unique, up to the order of the factors |
| gptkbp:usedIn |
cryptography
modular arithmetic greatest common divisor least common multiple |
| gptkbp:bfsParent |
gptkb:Number_theory
|
| gptkbp:bfsLayer |
5
|