number theory, the Fermat–Catalan conjecture is a generalization of Fermat's Last Theorem and of Catalan's conjecture. The conjecture states that the equation...
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In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b...
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Catalan's conjecture (or Mihăilescu's theorem) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1844...
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{1}{z}}<1} . Beal's conjecture can be restated as "All Fermat–Catalan conjecture solutions will use 2 as an exponent". The abc conjecture would imply that...
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Theorem for n ≥ 6 {\displaystyle n\geq 6} . The Fermat–Catalan conjecture, a generalization of Fermat's Last Theorem concerning powers that are sums of powers...
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Catalan pseudoprime Catalan's triangle Catalan–Dickson conjecture Catalan–Mersenne number conjecture Catalan beta function Fermat–Catalan conjecture Fuss–Catalan...
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including Roth's theorem, the Mordell conjecture, the Fermat–Catalan conjecture, and Brocard's problem. The conjecture states that: given ε > 0, there exists...
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de Fermat, a French amateur mathematician. Fermat–Apollonius circle Fermat–Catalan conjecture Fermat cubic Fermat curve Fermat–Euler theorem Fermat number...
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Double Mersenne number (redirect from Catalan–Mersenne number conjecture)
the Goldbach conjecture". In the movie, this number is known as a "Martian prime". Cunningham chain Double exponential function Fermat number Perfect...
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Fermat conjectured that all numbers of the form 2 2 m + 1 {\displaystyle 2^{2^{m}}+1} (known as Fermat numbers) were prime. However, this conjecture was...
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Ramanujan–Nagell equation, 2n − 7 = x2 the equation of the Fermat–Catalan conjecture and Beal's conjecture, am + bn = ck with inequality restrictions on the exponents...
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powers conjecture (disproved) concerns situations in which the sum of n integers, each a kth power of an integer, equals another kth power. The Fermat-Catalan...
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(Solomon W. Golomb, 1963) Fermat numbers and Fermat primes were first studied by Pierre de Fermat, who conjectured that all Fermat numbers are prime. Indeed...
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List of unsolved problems in mathematics (category Conjectures)
/ n = 1 / x + 1 / y + 1 / z {\displaystyle 4/n=1/x+1/y+1/z} . Fermat–Catalan conjecture: there are finitely many distinct solutions ( a m , b n , c k...
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The equations are generalisations of those considered in Fermat's Last Theorem. The conjecture is that if the sum of some k-th powers equals the sum of...
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equation appears in various contexts in elementary geometry. The Fermat–Catalan conjecture concerns a certain Diophantine equation, equating the sum of two...
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z} are required to be positive integers. The equation of the Fermat–Catalan conjecture: a m + b n = c k , {\displaystyle a^{m}+b^{n}=c^{k},} in which...
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in number theory including Roth's theorem, the Mordell conjecture, the Fermat–Catalan conjecture, and Brocard's problem. After moving to the CUNY Graduate...
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{\displaystyle k} a nonnegative integer. They are named after Pierre de Fermat, who conjectured that all such numbers are prime. The first five of these numbers...
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Carmichael number (redirect from Absolute Fermat pseudoprime)
had referred to them in 1948 as numbers with the "Fermat property", or "F numbers" for short. Fermat's little theorem states that if p {\displaystyle p}...
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Mordell curve Fermat's Last Theorem Mordell conjecture Euler's sum of powers conjecture abc Conjecture Catalan's conjecture Pillai's conjecture Hasse principle...
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example of 121 being one of the few numbers supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form...
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problem). Fermat knew that a fourth power cannot be the sum of two other fourth powers (the n = 4 case of Fermat's Last Theorem; see Fermat's right triangle...
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Bertrand's postulate (redirect from Bertrand's conjecture)
integers 2 ≤ n ≤ 3 000 000 {\displaystyle 2\leq n\leq 3\,000\,000} . His conjecture was completely proved by Chebyshev (1821–1894) in 1852 and so the postulate...
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Wieferich prime (category Abc conjecture)
of the ABC Conjecture using integer k'th roots" (PDF), New Zealand J. Math., 35 (2): 121–136 Ribenboim, P. (1979). 13 Lectures on Fermat's Last Theorem...
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proves the Mordell conjecture and thereby shows that there are only finitely many whole number solutions for each exponent of Fermat's Last Theorem. 1984 –...
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part of the Taniyama–Shimura conjecture and thereby proves Fermat's Last Theorem. 1999 — the full Taniyama–Shimura conjecture is proved. 2002 — Manindra...
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Fortunate number (redirect from Fortune's conjecture)
problem in mathematics: Are any Fortunate numbers composite? (Fortune's conjecture) (more unsolved problems in mathematics) A Fortunate number, named after...
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Mersenne prime (section Mersenne–Fermat primes)
(sequence A222119 in the OEIS) Repunit Fermat number Power of two Erdős–Borwein constant Mersenne conjectures Mersenne twister Double Mersenne number...
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Repunit (section The generalized repunit conjecture)
and 8191 (111 in base-90, 1111111111111 in base-2). The Goormaghtigh conjecture says there are only these two cases. Using the pigeon-hole principle it...
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