Fermat's Last Theorem

E146188
mathematical theorem

Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.

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All labels observed (5)

Label Occurrences
Fermat's Last Theorem canonical 3
Fermat’s Last Theorem 2
Fermat problem 1

Statements (48)

Predicate Object
instanceOf mathematical theorem ⓘ
allowsSolutionsFor n = 1 ⓘ
n = 2 ⓘ
alsoKnownAs Fermat's Last Theorem ⓘ
surface form: Fermat's conjecture
assertsNonexistenceOf nontrivial integer solutions for x^n + y^n = z^n with n > 2 ⓘ
classification Diophantine equation problem ⓘ
conditionOnExponent n is an integer greater than 2 ⓘ
conjectureDateApproximate circa 1637 ⓘ
conjecturedBy Pierre de Fermat ⓘ
correctedProofPublicationYear 1995 ⓘ
culturalImpact one of the most famous problems in mathematics ⓘ
difficulty famously difficult problem in mathematics ⓘ
domainOfVariables integers ⓘ
whole numbers ⓘ
equationForm x^n + y^n = z^n ⓘ
equivalentTo nonexistence of certain semistable elliptic curves over the rationals ⓘ
exponent n ⓘ
field number theory ⓘ
historicalStatus last of Fermat's conjectures to be proved ⓘ
influencedField algebraic number theory ⓘ
arithmetic geometry ⓘ
modular forms theory ⓘ
languageOfOriginalNote Latin ⓘ
namedAfter Pierre de Fermat ⓘ
openProblemDuration over 350 years ⓘ
originalClaim Fermat claimed to have a marvelous proof too large to fit in the margin ⓘ
originalSource margin note in Fermat's copy of Diophantus's Arithmetica ⓘ
proofAnnouncementYear 1993 ⓘ
proofCompletedWith Richard Taylor ⓘ
proofPublishedIn Annals of Mathematics ⓘ
proofRecognition contributed to Andrew Wiles receiving the Abel Prize in 2016 ⓘ
proofStrategy proof of a special case of the Taniyama–Shimura–Weil conjecture ⓘ
proofUses Galois representations ⓘ
elliptic curves ⓘ
modular forms ⓘ
provedBy Andrew Wiles ⓘ
relatedConjecture Taniyama–Shimura–Weil conjecture ⓘ
modularity theorem ⓘ
relatedProblem Beal conjecture ⓘ
abc conjecture ⓘ
solutionTypeExcluded nonzero integer solutions for n > 2 ⓘ
specialCaseFor Pythagorean triples when n = 2 ⓘ
statement There are no three positive integers x, y, z that satisfy x^n + y^n = z^n for any integer n > 2 ⓘ
statusAfter1990s proved theorem ⓘ
statusBefore1990s unproved conjecture ⓘ
variable x ⓘ
y ⓘ
z ⓘ

Referenced by (8)

Full triples — surface form annotated when it differs from this entity's canonical label.

Pierre de Fermat → notableWork → Fermat's Last Theorem ⓘ
Fermat's Last Theorem → alsoKnownAs → Fermat's Last Theorem ⓘ
this entity surface form: Fermat's conjecture
Fermat point → relatedConcept → Fermat's Last Theorem ⓘ
this entity surface form: Fermat problem
Fermat curve → relatedToConjecture → Fermat's Last Theorem ⓘ
this entity surface form: Fermat’s Last Theorem
Simon Singh → notableWork → Fermat's Last Theorem ⓘ
Simon Singh → authorOf → Fermat's Last Theorem ⓘ
Fermat Prize → relatedTo → Fermat's Last Theorem ⓘ
this entity surface form: Pierre de Fermat’s last theorem
Silver Plaque of the International Mathematical Union → associatedWith → Fermat's Last Theorem ⓘ
this entity surface form: Fermat’s Last Theorem