Fermat's theorem on the sum of two forty-ninth powers

GPTKB entity

Statements (70)
Predicate Object
gptkbp:instance_of gptkb:theorem
gptkbp:applies_to natural numbers.
gptkbp:challenges to prove.
for mathematicians.
to apply.
to understand.
gptkbp:field number theory
gptkbp:has_applications_in cryptography.
gptkbp:has_connection_to modular forms.
gptkbp:has_implications_for Implications for elliptic curves.
https://www.w3.org/2000/01/rdf-schema#label Fermat's theorem on the sum of two forty-ninth powers
gptkbp:inspired Further research in Diophantine equations.
gptkbp:is a conjecture.
gptkbp:is_a theorem in mathematics.
gptkbp:is_analyzed_in academic journals.
academic discussions.
research studies.
mathematical critiques.
gptkbp:is_cited_in research papers.
textbooks.
scholarly articles.
numerous mathematical works.
gptkbp:is_considered a fundamental theorem.
a significant theorem.
a classic result.
a landmark result.
a pivotal theorem.
a special case of Fermat's Last Theorem.
gptkbp:is_debated_in gptkb:1994
gptkbp:is_discussed_in academic papers.
mathematical literature.
academic circles.
mathematical forums.
mathematical conferences.
gptkbp:is_explored_in mathematical literature.
mathematical research.
mathematical theory.
mathematicians.
graduate studies.
gptkbp:is_influential_in modern number theory.
gptkbp:is_notable_for its historical significance.
its historical context.
its implications in mathematics.
its mathematical depth.
gptkbp:is_noted_for its complexity.
gptkbp:is_part_of the history of mathematics.
the study of number theory.
the legacy of Pierre de Fermat.
Fermat's conjectures.
the history of Fermat's work.
the legacy of number theory.
gptkbp:is_related_to the exploration of mathematical proofs.
the study of prime numbers.
the study of integer solutions.
the theory of equations.
the field of algebra.
Fermat's theorem on sums of two cubes.
gptkbp:is_standardized_by Fermat's Last Theorem for n=49.
gptkbp:is_studied_in higher education.
theoretical mathematics.
advanced mathematics courses.
algebraic geometry.
gptkbp:issues 49th powers
gptkbp:part_of Fermat's Last Theorem family.
gptkbp:proposed_by gptkb:Pierre_de_Fermat
gptkbp:proven_by gptkb:Andrew_Wiles
gptkbp:related_to gptkb:Fermat's_Last_Theorem
gptkbp:state There are no three positive integers a, b, and c that satisfy a^49 + b^49 = c^49.
gptkbp:bfsParent gptkb:Fermat
gptkbp:bfsLayer 5