• 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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  • Thumbnail for Eugène Charles Catalan
    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,...
    5 KB (354 words) - 21:39, 27 May 2025
  • 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...
    5 KB (710 words) - 10:08, 25 May 2025
  • Conjectures concerning the Mersenne numbers. Mathematics of Computation vol. 9 (1955) p. 120-121 [retrieved 2012-10-19] Weisstein, Eric W. "Catalan-Mersenne...
    10 KB (1,021 words) - 12:40, 26 March 2025
  • perfect number, or a set of amicable or sociable numbers? (Catalan's aliquot sequence conjecture) More unsolved problems in mathematics In mathematics, an...
    10 KB (1,331 words) - 10:57, 18 January 2025
  • Thumbnail for Fermat's Last Theorem
    In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b,...
    104 KB (11,728 words) - 19:17, 8 June 2025
  • 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...
    25 KB (3,378 words) - 00:32, 13 May 2025
  • 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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  • Thumbnail for Abc conjecture
    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...
    42 KB (4,598 words) - 06:52, 31 May 2025
  • is prime infinitely often. Catalan's Mersenne conjecture: some Catalan–Mersenne number is composite and thus all Catalan–Mersenne numbers are composite...
    195 KB (20,026 words) - 13:12, 7 May 2025
  • test, and Preda Mihăilescu created a proof for the 150-year-old Catalan's conjecture.: 261  The September 11 attacks of the previous year caused a shift...
    130 KB (12,756 words) - 14:28, 6 June 2025
  • Thumbnail for Catalan's constant
    Catalan's constant. These results by Wadim Zudilin and Tanguy Rivoal are related to similar ones given for the odd zeta constants ζ(2n+1). Catalan's constant...
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  • Thumbnail for Diophantine equation
    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...
    33 KB (4,809 words) - 12:42, 14 May 2025
  • number's digits, making 121 a self number. Ribenboim, Paulo (1994). Catalan's conjecture : are 8 and 9 the only consecutive powers?. Boston: Academic Press...
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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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  • conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...
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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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  • 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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  • 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...
    4 KB (490 words) - 05:32, 11 August 2024
  • 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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  • Gillies' conjecture on the distribution of numbers of prime factors of Mersenne numbers Lucas–Lehmer primality test Lucas primality test Catalan's Mersenne...
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  • Thumbnail for Perfect power
    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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  • Thumbnail for Paderborn University
    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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  • Casimir effect – Hendrik Casimir Catalan's conjecture (a.k.a. Mihăilescu's theorem), Catalan numbers – Eugène Charles Catalan Cauchy number (a.k.a. Hooke number)...
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  • Thumbnail for René Schoof
    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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  • applications of it." Chein (1976) used Størmer's method to prove Catalan's conjecture on the nonexistence of consecutive perfect powers (other than 8,9)...
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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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  • test). 2002 – Preda Mihăilescu proves Catalan's conjecture. 2003 – Grigori Perelman proves the Poincaré conjecture. 2004 – the classification of finite...
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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...
    13 KB (1,403 words) - 18:16, 8 April 2025