Fermat's theorem on sums of two squares
GPTKB entity
Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
prime numbers
|
| gptkbp:category |
theorems in number theory
|
| gptkbp:field |
number theory
|
| gptkbp:generalizes |
gptkb:Brahmagupta–Fibonacci_identity
|
| gptkbp:hasProof |
elementary proof
proof using Gaussian integers |
| https://www.w3.org/2000/01/rdf-schema#label |
Fermat's theorem on sums of two squares
|
| gptkbp:implies |
If p ≡ 3 mod 4, p cannot be written as a sum of two squares.
|
| gptkbp:namedAfter |
gptkb:Pierre_de_Fermat
|
| gptkbp:provenBy |
gptkb:Euler
|
| gptkbp:publishedIn |
17th century
|
| gptkbp:relatedTo |
gptkb:Fermat's_Last_Theorem
sum of two squares theorem |
| gptkbp:state |
An odd prime p can be expressed as the sum of two squares if and only if p ≡ 1 mod 4.
|
| gptkbp:bfsParent |
gptkb:Primes_of_the_Form_x^2_+_ny^2
|
| gptkbp:bfsLayer |
6
|