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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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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famous Catalan's conjecture, which was eventually proved in 2002; and introducing the Catalan numbers to solve a combinatorial problem. Catalan was born...
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Mihăilescu proved Catalan's conjecture. This number-theoretical conjecture, formulated by the French and Belgian mathematician Eugène Charles Catalan in 1844,...
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Double Mersenne number (redirect from Catalan's Mersenne conjecture)
Conjectures concerning the Mersenne numbers. Mathematics of Computation vol. 9 (1955) p. 120-121 [retrieved 2012-10-19] Weisstein, Eric W. "Catalan-Mersenne...
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Aliquot sequence (redirect from Catalan's aliquot sequence conjecture)
perfect number, or a set of amicable or sociable numbers? (Catalan's aliquot sequence conjecture) (more unsolved problems in mathematics) In mathematics...
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problems Catalan solids, a family of polyhedra Catalan's constant, a number that occurs in estimates in combinatorics Catalan's conjecture Catalan (grape)...
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conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...
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64 The impossibility of the case A = 1 or B = 1 is implied by Catalan's conjecture, proven in 2002 by Preda Mihăilescu. (Notice C cannot be 1, or one...
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The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and...
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if CFOP is used for their 3x3x3 stages. He also wrote a book on Catalan's conjecture. Schoof's algorithm Schoof–Elkies–Atkin algorithm Homepage Counting...
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List of unsolved problems in mathematics (category Conjectures)
is prime infinitely often. Catalan's Mersenne conjecture: some Catalan–Mersenne number is composite and thus all Catalan–Mersenne numbers are composite...
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Fermat's Last Theorem (redirect from Fermat conjecture)
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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theory for such equations is not available; particular cases such as Catalan's conjecture and Fermat's Last Theorem have been tackled. However, the majority...
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Fermat's Last Theorem Mordell conjecture Euler's sum of powers conjecture abc Conjecture Catalan's conjecture Pillai's conjecture Hasse principle Diophantine...
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Tijdeman's theorem (category Abc conjecture)
theorem provided a strong impetus towards the eventual proof of Catalan's conjecture by Preda Mihăilescu. Mihăilescu's theorem states that there is only...
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Mihăilescu, Preda (2004). "Primary Cyclotomic Units and a Proof of Catalan's Conjecture". J. Reine Angew. Math. 572. Berlin: De Gruyter: 167–195. doi:10...
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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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Nations Security Council Resolution 121 Ribenboim, Paulo (1994). Catalan's conjecture : are 8 and 9 the only consecutive powers?. Boston: Academic Press...
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on quadratic forms, the Erdős–Ko–Rado theorem and his theorem on Catalan's conjecture. In 1955, he was one of the founding members of the Chinese Academy...
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tissues other than nervous. Preda Mihăilescu: known for his proof of Catalan's conjecture. Meinhard E. Mayer: an early contributor to the theory of vector-bosons...
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In mathematics, Catalan's constant G, is defined by G = β ( 2 ) = ∑ n = 0 ∞ ( − 1 ) n ( 2 n + 1 ) 2 = 1 1 2 − 1 3 2 + 1 5 2 − 1 7 2 + 1 9 2 − ⋯ , {\displaystyle...
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Mihăilescu's 2002 proof of Mihăilescu's theorem (formerly known as Catalan's conjecture). There are only 7 Wieferich pairs known: (2, 1093), (3, 1006003)...
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whether a given number is prime. 2002 — Preda Mihăilescu proves Catalan's conjecture. 2004 — Ben Green and Terence Tao prove the Green–Tao theorem, which...
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consecutive perfect powers is 23 = 8 and 32 = 9, thus proving Catalan's conjecture. Pillai's conjecture states that for any given positive integer k there are...
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The Lander, Parkin, and Selfridge conjecture concerns the integer solutions of equations which contain sums of like powers. The equations are generalisations...
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each a kth power of an integer, equals another kth power. The Fermat-Catalan conjecture asks whether there are an infinitude of examples in which the sum...
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theory. He was elected a member of the Académie des sciences in 1847. Catalan's conjecture Proof of Fermat's Last Theorem for specific exponents Lebesgue–Nagell...
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proved the Catalan conjecture, a number-theoretical conjecture, formulated by the French and Belgian mathematician Eugène Charles Catalan, which had stood...
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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 the...
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