Wall-Sun-Sun prime

In mathematics, a Wilson prime is a certain kind of prime number. A prime p is called a Wilson prime if p² divides (p − 1)! + 1, where ! denotes the factorial function; compare this with Wilson's theorem, which states that every prime p divides (p − 1)! + 1. The only known Wilson primes are 5, 13, and 563 (sequence A007540 in OEIS); if any others exist, they must be greater than 5 · 108. It has been conjectured that infinitely many Wilson primes exist, and that the number of Wilson primes in an interval [x, ...

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Fermat's last theorem - Fermat's comment in the Arithmetica. In problem II.8 of his Arithmetica, Diophantus asks how to split a given square number into two other squares (in modern notation, given a rational number k, find u and v, both rational, such that k2 = u2 + v2), and shows how to solve the problem for See also:

Fermat's last theorem, Fermat's last theorem - History, Fermat's last theorem - Fermat's comment in the Arithmetica, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

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This is the note that Fermat wrote in the margin of Arithmetica: Cubum autem in duos cubos, aut quadrato-quadratum in duos quadrato-quadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet. (It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. I have discovered a truly ma ...

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Fermat's last theorem, Fermat's last theorem - Mathematical context, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

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There is considerable doubt over whether Fermat's claim to have "a truly marvellous proof" was correct. Wiles's proof is about 200 pages long and beyond the understanding of most mathematicians today. It is quite possible that there is a proof that is both essentially shorter, and more elementary in its methods; initial proofs of major results are typically not the most direct. Math institutions still receive many papers, some say in the thousands, claiming t ...

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Fermat's last theorem, Fermat's last theorem - History, Fermat's last theorem - Fermat's comment in the Arithmetica, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

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In "The Royale", an episode of Star Trek: The Next Generation, Captain Picard states that the theorem had gone unsolved for 800 years. Wiles' proof was released five years after the particular episode aired. This was subsequently mentioned in a Star Trek: Deep Space Nine episode called "Facets" during June 1995 in which Jadzia Dax comments that one of her previous hosts, Tobin Dax, had "the most original approach to the proof since Wiles over 300 years ago." [4] This reference was generally understood by ...

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Fermat's last theorem, Fermat's last theorem - History, Fermat's last theorem - Fermat's comment in the Arithmetica, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

Read more here: » Fermat's last theorem: Encyclopedia II - Fermat's last theorem - Trivia

In "The Royale", an episode of Star Trek: The Next Generation, Captain Picard states that the theorem had gone unsolved for 800 years. Wiles' proof was released five years after the particular episode aired. This was subsequently mentioned in a Star Trek: Deep Space Nine episode called "Facets" during June 1995 in which Jadzia Dax comments that one of her previous hosts, Tobin Dax, had "the most original approach to the proof since Wiles over 300 years ago." [4] This reference was generally understood by ...

See also:

Fermat's last theorem, Fermat's last theorem - Mathematical context, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

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The theorem needs only to be proven for n=4 and in the cases where n is an odd prime number.[2] For various special exponents n, the theorem had been proven over the years, but the general case remained elusive. Fermat himself proved the case n=4, while Euler proved the theorem for n=3. The case n=5 was proved by Dirichlet and Legendre in ...

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Fermat's last theorem, Fermat's last theorem - Mathematical context, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

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Using sophisticated tools from algebraic geometry (in particular elliptic curves and modular forms), Galois theory and Hecke algebras, the English mathematician Andrew Wiles, from Princeton University, with help from his former student Richard Taylor, devised a proof of Fermat's last theorem that was published in 1995 in the journal Annals of Mathematics. In 1986, Ken Ribet had proved Gerhard Frey's epsilon conjecture that every counterexample an + bn = cn to Fermat's las ...

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Fermat's last theorem, Fermat's last theorem - Mathematical context, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

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Fermat's last theorem is a generalization of the Diophantine equation a2 + b2 = c2, which is linked to the Pythagorean theorem. Ancient Chinese, Greeks and Babylonians knew that this equation has integer solutions, such as (3,4,5) (32 + 42 = 52) or (5,12,13). These solutions are known as Pythagorean triples, and there exist an infinite number of them (even excluding trivial solutions for which a, b and c have a common divisor). According to Fermat's last theorem, no such soluti ...

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Fermat's last theorem, Fermat's last theorem - Mathematical context, Fermat's last theorem - Early history, Fermat's last theorem - The proof, Fermat's last theorem - Did Fermat really have a proof?, Fermat's last theorem - Trivia, Fermat's last theorem - Notes, Fermat's last theorem - Bibliography and further reading

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List of number theory topics - Primality tests. Prime factorization algorithm Trial division Sieve of Eratosthenes Probabilistic algorithm Fermat primality test Pseudoprime Carmichael number Euler pseudoprime Euler-Jacobi pseudoprime Fibonacci pseudoprime Probable prime Miller-Rabin primality test Lucas-Lehmer primality test Lucas-Lehmer test for Mersenne numbers AKS prim ...

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List of number theory topics, List of number theory topics - Factors, List of number theory topics - Fractions, List of number theory topics - Modular arithmetic, List of number theory topics - Arithmetic functions, List of number theory topics - Analytic number theory: additive problems, List of number theory topics - Algebraic number theory, List of number theory topics - Quadratic forms, List of number theory topics - L-functions, List of number theory topics - Diophantine equations, List of number theory topics - Diophantine approximation, List of number theory topics - Sieve methods, List of number theory topics - Named primes, List of number theory topics - Combinatorial number theory, List of number theory topics - Computational number theory, List of number theory topics - Primality tests, List of number theory topics - Integer factorization, List of number theory topics - Pseudo-random numbers, List of number theory topics - History

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