Fermat's theorem on sums of two squares
GPTKB entity
Statements (65)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:bfsLayer |
5
|
| gptkbp:bfsParent |
gptkb:Pierre_de_Fermat
gptkb:Fermat |
| gptkbp:applies_to |
prime numbers
|
| gptkbp:has |
13 = 2^2 + 3^2
29 = 2^2 + 5^2 41 = 4^2 + 5^2 5 = 1^2 + 2^2 61 = 5^2 + 6^2 |
| gptkbp:has_programs |
gptkb:Mathematician
|
| gptkbp:historical_debate |
gptkb:Jacobi's_four-square_theorem
|
| gptkbp:historical_significance |
17th century mathematics
|
| https://www.w3.org/2000/01/rdf-schema#label |
Fermat's theorem on sums of two squares
|
| gptkbp:is_a |
special case of Waring's problem
|
| gptkbp:is_analyzed_in |
mathematical journals
mathematical textbooks academic lectures mathematical reviews |
| gptkbp:is_cited_in |
gptkb:Pierre_de_Fermat
research articles academic papers mathematical proofs textbooks on number theory dissertations |
| gptkbp:is_connected_to |
Pythagorean triples
Lagrange's four-square theorem |
| gptkbp:is_described_as |
mathematical induction
|
| gptkbp:is_discussed_in |
mathematical literature
mathematical discussions mathematical seminars mathematical blogs historical mathematics texts online mathematics forums |
| gptkbp:is_explored_in |
mathematical conferences
undergraduate mathematics courses advanced number theory courses graduate mathematics programs number theory research historical mathematics research |
| gptkbp:is_influential_in |
modern mathematics
|
| gptkbp:is_part_of |
gptkb:Fermat's_work_on_number_theory
gptkb:Fermat's_legacy gptkb:Fermat's_Last_Theorem the history of mathematics the study of prime numbers Fermat's contributions to mathematics |
| gptkbp:is_related_to |
gptkb:Gaussian_integers
gptkb:Diophantine_equations complex numbers modular arithmetic algebraic number theory analytic number theory quadratic forms integer factorization |
| gptkbp:is_used_in |
gptkb:currency
theoretical computer science algorithm design mathematical modeling mathematical competitions combinatorial number theory mathematical proofs and derivations |
| gptkbp:related_to |
number theory
|
| gptkbp:state |
A prime number p can be expressed as a sum of two squares if and only if p = 2 or p ≡ 1 (mod 4).
|
| gptkbp:training |
university mathematics courses
|