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17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
1995 publication in mathematics
Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
French mathematician and lawyer (1601–1665)
probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in
Pierre_de_Fermat
A prime p divides a^p–a for any integer a
Pierre de Fermat, who stated it in 1640. It is called the "little theorem" to distinguish it from Fermat's Last Theorem. Pierre de Fermat first stated
Fermat's_little_theorem
Non-fiction book by Simon Singh
Fermat's Last Theorem is a popular science book (1997) by Simon Singh. It tells the story of the search for a proof of Fermat's Last Theorem, first conjectured
Fermat's_Last_Theorem_(book)
References to the famous problem in number theory
as "Fermat's Last Theorem" has repeatedly received attention in fiction and popular culture. It was proved by Andrew Wiles in 1994. The theorem plays
Fermat's Last Theorem in fiction
Fermat's_Last_Theorem_in_fiction
Index of articles associated with the same name
mathematician Pierre de Fermat engendered many theorems. Fermat's theorem may refer to one of the following theorems: Fermat's Last Theorem, about integer solutions
Fermat's_theorem
2008 novel by Arthur C. Clarke and Frederik Pohl
about a young Sri Lankan mathematician who finds a short proof of Fermat's Last Theorem, while an alien invasion of Earth is in progress. The novel began
The_Last_Theorem
2000 off-Broadway musical
Fermat's Last Tango is a 2000 off-Broadway musical about the proof of Fermat's Last Theorem, written by husband and wife Joshua Rosenblum (music, lyrics)
Fermat's_Last_Tango
Topics referred to by the same term
Proof of Fermat's last theorem may refer to: Wiles's proof of Fermat's Last Theorem Proof of Fermat's Last Theorem for specific exponents This disambiguation
Proof of Fermat's Last Theorem
Proof_of_Fermat's_Last_Theorem
American columnist, author and lecturer (born 1946)
proved Fermat's Last Theorem, Savant published the book The World's Most Famous Math Problem (October 1993), which surveys the history of Fermat's Last Theorem
Marilyn_vos_Savant
British mathematician who proved Fermat's Last Theorem
Oxford, specialising in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley
Andrew_Wiles
Rational right triangles cannot have square area
Fermat's right triangle theorem is a non-existence proof in number theory, published in 1670 among the works of Pierre de Fermat, soon after his death
Fermat's right triangle theorem
Fermat's_right_triangle_theorem
Relates rational elliptic curves to modular forms
Richard Taylor proved the modularity theorem for semistable elliptic curves, which was enough to imply Fermat's Last Theorem (FLT). Later, a series of papers
Modularity_theorem
On the divisibility of solutions to Fermat's Last Theorem for prime exponent
theorem is a statement about the divisibility of solutions to the equation x p + y p = z p {\displaystyle x^{p}+y^{p}=z^{p}} of Fermat's Last Theorem
Sophie_Germain's_theorem
British physicist and popular science author (born 1964)
particle physicist. His written works include Fermat's Last Theorem (in the United States titled Fermat's Enigma: The Epic Quest to Solve the World's Greatest
Simon_Singh
Polynomial equation whose integer solutions are sought
conjecture and Fermat's Last Theorem have been tackled. However, the majority are solved via ad-hoc methods such as Størmer's theorem or even trial and
Diophantine_equation
Generalization of Fermat's Last Theorem and of Catalan's conjecture,
In number theory, the Fermat–Catalan conjecture is a generalization of Fermat's Last Theorem and of Catalan's conjecture. The conjecture states that the
Fermat–Catalan_conjecture
French mathematician, physicist, and philosopher (1776–1831)
Paris Academy of Sciences for her essay on the subject. Her work on Fermat's Last Theorem provided a foundation for mathematicians exploring the subject for
Sophie_Germain
Partial results found before the complete proof
Fermat's Last Theorem is a theorem in number theory, originally stated by Pierre de Fermat in 1637 and proven by Andrew Wiles in 1995. The statement of
Proof of Fermat's Last Theorem for specific exponents
Proof_of_Fermat's_Last_Theorem_for_specific_exponents
Condition under which an odd prime is a sum of two squares
In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2}
Fermat's theorem on sums of two squares
Fermat's_theorem_on_sums_of_two_squares
Integers have unique prime factorizations
mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Prime such that p^2 divides 2^(p-1)-1
Arthur Wieferich in 1909 in works pertaining to Fermat's Last Theorem, at which time both of Fermat's theorems were already well known to mathematicians. Since
Wieferich_prime
Proof assistant and programming language
Fable 5.1 had produced a complete, machine-checked formalization of Fermat's Last Theorem in Lean 4 in eleven days. The proof followed the 1995 exposition
Lean_(proof_assistant)
In mathematics, a statement that has been proven
disparate areas of mathematics. Fermat's Last Theorem is a particularly well-known example of such a theorem. Logically, many theorems are of the form of an indicative
Theorem
Mathematical polynomial formula
for "Same, Opposite, Always Positive", helps recall of the signs: Fermat's Last Theorem in the case of exponent 3 states that the sum of two non-zero integer
Sum_of_two_cubes
Branch of pure mathematics
understand but are very difficult to solve. Examples of this are Fermat's Last Theorem, which was proved 358 years after the original formulation, and
Number_theory
Proposition in mathematics that is unproven
proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical
Conjecture
Integer side lengths of a right triangle
greater than 2. Pierre de Fermat in 1637 claimed that no such triple exists, a claim that came to be known as Fermat's Last Theorem because it took longer
Pythagorean_triple
On properties of Galois representations associated with modular forms
Ken Ribet. The proof was a significant step towards the proof of Fermat's Last Theorem (FLT). As shown by Serre and Ribet, the Taniyama–Shimura conjecture
Ribet's_theorem
Conjecture in number theory
proof of Fermat's Last Theorem for n ≥ 6 {\displaystyle n\geq 6} . The Fermat–Catalan conjecture, a generalization of Fermat's Last Theorem concerning
Abc_conjecture
German mathematician (1805–1859)
German mathematician. In number theory, he proved special cases of Fermat's Last Theorem and created analytic number theory. In analysis, he advanced the
Peter Gustav Lejeune Dirichlet
Peter_Gustav_Lejeune_Dirichlet
Disproved conjecture in number theory
theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem. It was presented by Leonhard Euler in 1778 to the Academy of Sciences
Euler's sum of powers conjecture
Euler's_sum_of_powers_conjecture
36 mathematical problems stated in 1955
conjecture, also known as the modularity theorem, which would be used in Andrew Wiles' proof of Fermat's Last Theorem in 1995. In the 1950s post-World War
Taniyama's_problems
American banker, businessman, investor, and amateur mathematician
known for the Beal conjecture, a mathematical generalization of Fermat's Last Theorem. He has funded a $1 million standing prize for its proof or disproof
Andrew_Beal
Elliptic curve associated with a Fermat triple
popularized in its application to Fermat’s Last Theorem where one investigates a (hypothetical) solution of Fermat's equation a ℓ + b ℓ = c ℓ . {\displaystyle
Frey_curve
Branch of number theory
theorem in diophantine approximation, later named after him Dirichlet's approximation theorem. He published important contributions to Fermat's last theorem
Algebraic_number_theory
Basic Introduction
Langlands–Tunnell theorem is a theorem due to Robert Langlands and Jerrold Tunnell that played a fundamental role in Wiles's proof of Fermat's last theorem. The theorem
Langlands–Tunnell_theorem
Nigerian politician and mathematician
solve Fermat’s Last Theorem after Andrew Wiles and Richard Taylor in 1994. He also claimed to have found an elementary proof to Fermat’s Last Theorem. This
Chike_Obi
Theorem in number theory
among them Fermat's Last Theorem and the now-proven Taniyama–Weil (or Taniyama–Shimura) conjecture, now known as the modularity theorem (although this
Serre's_modularity_conjecture
Relation between sides of a right triangle
British flag theorem Bride's Chair – Illustration of the Pythagorean theorem Fermat's Last Theorem Garfield's proof of the Pythagorean theorem Hsuan thu –
Pythagorean_theorem
Concept in Number Theory
quotient is named after Pierre de Fermat. If the base a is coprime to the exponent p then Fermat's little theorem says that qp(a) will be an integer
Fermat_quotient
American mathematician
known for the Herbrand–Ribet theorem and Ribet's theorem, which were key ingredients in the proof of Fermat's Last Theorem, as well as for his service
Ken_Ribet
Prime pair of the form (p, 2p+1)
who used them in her investigations of Fermat's Last Theorem. One attempt by Germain to prove Fermat's Last Theorem was to let p be a prime number of the
Safe and Sophie Germain primes
Safe_and_Sophie_Germain_primes
Algebraic curve
the Fermat equation would correspond to a nonzero rational number solution to the affine equation, and vice versa. But by Fermat's Last Theorem it is
Fermat_curve
Number raised to the third power
for the last two digits. Except for cubes divisible by 5, where only 25, 75 and 00 can be the last two digits, any pair of digits with the last digit odd
Cube_(algebra)
al-Khujandi first states a special case of Fermat's Last Theorem. 895 — Thabit ibn Qurra gives a theorem by which pairs of amicable numbers can be found
Timeline_of_number_theory
Conjecture in number theory
and amateur mathematician, while investigating generalizations of Fermat's Last Theorem. Since 1997, Beal has offered a monetary prize for a peer-reviewed
Beal_conjecture
Book by Hiroshi Yūki
Creative in 2007, followed by Math Girls: Fermat's Last Theorem in 2008, Math Girls: Gödel's Incompleteness Theorems in 2009, Math Girls: Randomized Algorithms
Math_Girls
Algebraic integer which represents an ideal in a ring of integers
interest in Fermat's Last Theorem; there is even a story often told that Kummer, like Lamé, believed he had proven Fermat's Last Theorem until Lejeune
Ideal_number
Type of prime number
number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class
Regular_prime
Equation of the form 1/a + 1/b = 1/c
or 2c. In other words, c is half the harmonic mean of a and b. Fermat's Last Theorem states that the sum of two integers each raised to the same integer
Optic_equation
American mathematician (born 1943)
for Andrew Wiles when Wiles was developing in secret his proof of Fermat's Last Theorem. Mathematician and cryptographer Neal Koblitz was one of Katz's
Nick_Katz
Chinese mathematician
Sun proved a theorem about what are now known as the Wall–Sun–Sun primes that guided the search for counterexamples to Fermat's Last Theorem. Zhi-Hong Sun's
Zhi-Hong_Sun
Indian mathematician (1887–1920)
Fields Medal-winning work) proved Serre's conjecture. The proof of Fermat's Last Theorem proceeds by first reinterpreting elliptic curves and modular forms
Srinivasa_Ramanujan
Number divisible only by 1 and itself
square roots modulo integer prime numbers. Early attempts to prove Fermat's Last Theorem led to Kummer's introduction of regular primes, integer prime numbers
Prime_number
British-American mathematician (born 1962)
JSTOR 2118560. Wiles, Andrew (1995). "Modular elliptic curves and Fermat's Last Theorem". Annals of Mathematics. 141 (3): 443–551. doi:10.2307/2118559.
Richard Taylor (mathematician)
Richard_Taylor_(mathematician)
American mathematician (1936–2020)
expository books on the Riemann zeta function, on Galois theory, and on Fermat's Last Theorem. He wrote a book on Leopold Kronecker's work on divisor theory providing
Harold Edwards (mathematician)
Harold_Edwards_(mathematician)
and Adrien-Marie Legendre prove Fermat's Last Theorem for n = 5. 1825 – André-Marie Ampère discovers Stokes' theorem. 1826 – Niels Henrik Abel gives counterexamples
Timeline_of_mathematics
This article collects together a variety of proofs of Fermat's little theorem, which states that a p ≡ a ( mod p ) {\displaystyle a^{p}\equiv a{\pmod
Proofs of Fermat's little theorem
Proofs_of_Fermat's_little_theorem
"Formalizing Fermat's Last Theorem". Archived from the original on 4 September 2026. Retrieved 5 September 2026. Anthropic. "Formalizing Fermat's Last Theorem in
List of mathematical discoveries by artificial intelligence
List_of_mathematical_discoveries_by_artificial_intelligence
2013 book by Simon Singh
mathematical topics, anecdotes and history". Topics covered include Fermat's Last Theorem, which Singh has written a popular book about, and Euler's identity
The Simpsons and Their Mathematical Secrets
The_Simpsons_and_Their_Mathematical_Secrets
Field extension of the rational numbers by a primitive root of unity
modern algebra and number theory because of their relation with Fermat's Last Theorem. It was in the process of his deep investigations of the arithmetic
Cyclotomic_field
American mathematician (born 1937)
include his contributions to Wiles's proof of Fermat's Last Theorem in number theory, Mazur's torsion theorem in arithmetic geometry, the Mazur swindle in
Barry_Mazur
Branch of mathematics
methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, a problem that was stated in terms of elementary arithmetic, and
Geometry
Unsolved problem in science and mathematics
"closed" by researchers in the late twentieth century are Fermat's Last Theorem and the four-color theorem. An important open mathematics problem solved in the
Open_problem
Set disjoint from its sumset with itself
.., 2N} forms a large sum-free subset of the set {1, ..., 2N}. Fermat's Last Theorem is the statement that, for a given integer n > 2, the set of all
Sum-free_set
Unsolved conjecture on equal sums of like powers
by Fermat's Last Theorem. Consequently, the first unresolved exponent is k = 5 {\displaystyle k=5} . For k = 5 {\displaystyle k=5} , Fermat's Last Theorem
Lander, Parkin, and Selfridge conjecture
Lander,_Parkin,_and_Selfridge_conjecture
Law in algebraic number theory
y z . {\displaystyle p\nmid xyz.\;\;} This is the first case of Fermat's Last Theorem. (The second case is when p ∣ x y z . {\displaystyle p\mid xyz.\;}
Eisenstein_reciprocity
German physician and mathematician
marks (equivalent to €720,000 in 2023) to the first person to prove Fermat's Last Theorem. He was the younger of two sons of a banker, Joseph Carl Theodor
Paul_Wolfskehl
French mathematician (born 1968)
semistable elliptic curves by Andrew Wiles and Taylor in their proof of Fermat's Last Theorem. Later, he worked on the p-adic Langlands conjecture. Breuil attended
Christophe_Breuil
1992 book by Underwood Dudley
trisection Fermat's Last Theorem Non-Euclidean geometry and the parallel postulate The golden ratio Perfect numbers The four color theorem Advocacy for
Mathematical_Cranks
Field of knowledge
mathematics. A prominent example is Fermat's Last Theorem. This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew
Mathematics
Japanese mathematician
Fermat's Last Theorem, which inspired Andrew Wiles to work for a number of years in secrecy on it, and to prove enough of it to prove Fermat's Last Theorem
Yutaka_Taniyama
Mathematical concept
theorem), implies Fermat's Last Theorem. Thus, if the Taniyama–Shimura conjecture is true for semistable elliptic curves, then Fermat's Last Theorem would
Modular_elliptic_curve
Australian-American mathematician
where he gave a lecture entitled "30 years of modularity since Fermat's Last Theorem." Calegari was awarded the 2026 Cole Prize in Number Theory jointly
Frank_Calegari
Branch of mathematics
cubic reciprocity law for the Eisenstein integers. The study of Fermat's Last Theorem led to the algebraic integers. In 1847, Gabriel Lamé thought he
Abstract_algebra
In algebraic geometry, a point with rational coordinates
theory and Diophantine geometry. For example, Fermat's Last Theorem may be restated as: for n > 2, the Fermat curve of equation x n + y n = 1 {\displaystyle
Rational_point
Positive integer of the form (2^(2^n))+1
discovered in October 2020. Heuristics suggest that F4 is the last Fermat prime. The prime number theorem implies that a random integer in a suitable interval
Fermat_number
UK educational YouTube channel (2011-)
advanced mathematical concepts such as Fermat's Last Theorem, the Riemann hypothesis and Kruskal's tree theorem. The videos are produced by Brady Haran
Numberphile
American popular science public television program (since 1974)
equation, elementary particles, the 1980 eruption of Mount St. Helens, Fermat's Last Theorem, the AIDS epidemic, global warming, moissanite, Project Jennifer
Nova_(American_TV_program)
American mathematician
Michigan and at Columbia University. Conrad and others proved the modularity theorem, also known as the Taniyama-Shimura Conjecture. He proved this in 1999
Brian_Conrad
French mathematician (1752–1833)
ellipsoids – appeared in the second volume. In 1830, he gave a proof of Fermat's Last Theorem for exponent n = 5, which was also proven by Lejeune Dirichlet in
Adrien-Marie_Legendre
Topics referred to by the same term
Wieferich's criterion for the solubility of the "First Case" of Fermat's Last Theorem The solution to Waring's problem for cubes, that every integer is
Wieferich's_theorem
In algebra, element without non-trivial factors
proofs of Fermat's Last Theorem that were given during the three centuries between Fermat's statement and Wiles's proof of Fermat's Last Theorem. If R {\displaystyle
Irreducible_element
Brazilian-Canadian mathematician
ISBN 978-0-387-97042-4. Paulo Ribenboim. (1995). 13 Lectures on Fermat's Last Theorem. Springer-Verlag. ISBN 978-0-387-90432-0. Paulo Ribenboim. (1996)
Paulo_Ribenboim
French mathematician (1795–1870)
also proved a special case of Fermat's Last Theorem. He actually thought that he found a complete proof for the theorem, but his proof was flawed. The
Gabriel_Lamé
threefold Fermat quotient Fermat's difference quotient Fermat's factorization method Fermat's Last Theorem Fermat's little theorem Fermat's method Fermat's method
List of things named after Pierre de Fermat
List_of_things_named_after_Pierre_de_Fermat
Book by Ian Stewart
conjecture Squaring the circle Four colour theorem Kepler's conjecture Mordell's conjecture Fermat's Last Theorem Three-body problem Riemann hypothesis Poincare
The Great Mathematical Problems
The_Great_Mathematical_Problems
Algebraic curve in mathematics
research; for example, they were used in Andrew Wiles's proof of Fermat's Last Theorem. They also find applications in elliptic curve cryptography (ECC)
Elliptic_curve
2008 film by Álex de la Iglesia
community is excited as a local researcher claims to have solved Fermat's Last Theorem. The mathematicians, including Seldom and Martin, board a bus to
The_Oxford_Murders_(film)
German mathematician (1912–1992)
corresponding modular form would later be the key to the proof of Fermat's Last Theorem. Quadratische Formen und orthogonale Gruppen, Springer 1952, 1974
Martin_Eichler
Result in number theory, concerning irreducible polynomials
large rank. Hilbert's irreducibility theorem is used as a step in the Andrew Wiles proof of Fermat's Last Theorem. If a polynomial g ( x ) ∈ Z [ x ] {\displaystyle
Hilbert's irreducibility theorem
Hilbert's_irreducibility_theorem
Russian mathematician (born 1955)
cyclotomic fields. His work also influenced Andrew Wiles's work on Fermat's Last Theorem. Kolyvagin received his Ph.D. in Mathematics in 1981 from Moscow
Victor_Kolyvagin
12th episode of the 2nd season of Star Trek: The Next Generation
Commander Riker about Fermat's Last Theorem, which in the canon of the series had remained unsolved for 800 years (the theorem was proved in 1995, six
The_Royale
Conjecture in number theory
number of consequences in number theory including Roth's theorem, Faltings' theorem, the Fermat–Catalan conjecture, and Brocard's problem. The conjecture
Szpiro's_conjecture
Topics referred to by the same term
FLT may refer to: Fermat's Last Theorem, in number theory Fermat's little theorem, using modular arithmetic Finite Legendre transform, in algebra Alovudine
FLT
Unsolved problem in computer science
prove theorems, and some proofs have taken decades or even centuries to find after problems have been stated—for instance, Fermat's Last Theorem took over
P_versus_NP_problem
American mathematician (born 1955)
ISBN 0-387-98981-1. ———; Cornell, G.; Stevens, G. (1997), Modular forms and Fermat's Last Theorem, Springer, ISBN 0-387-94609-8. ———; Hoffstein, J.; Pipher, J. (12
Joseph_H._Silverman
1941 book
in mathematics, including the proofs of the four-color map theorem and Fermat's last theorem, written by Ian Stewart. The book was based on Courant's course
What_Is_Mathematics?
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FERMATS LAST-THEOREM
FERMATS LAST-THEOREM
FERMATS LAST-THEOREM
FERMATS LAST-THEOREM
FERMATS LAST-THEOREM
FERMATS LAST-THEOREM
FERMATS LAST-THEOREM
FERMATS LAST-THEOREM
FERMATS LAST-THEOREM
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