Výsledky vyhledávání - "Catalan's conjecture"

Elektronická kniha

Autor: René Schoof

Eugène Charles Catalan made his famous conjecture – that 8 and 9 are the only two consecutive perfect powers of natural numbers – in 1844 in a letter to the editor of Crelle's mathematical journal. One hundred and fifty-eight years later, Preda

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On a criterion for Catalan's Conjecture

Autor: Schlage-Puchta, Jan-Christoph

Publikováno v: Ramanujan J. 5 (2001), no. 4, 405-407 (2002)

We give a new proof of a theorem by P. Mihailescu which states that the equation $x^p-y^q=1$ is unsolvable with $x, y$ integral and $p, q$ odd primes, unless the congruences $p^q \equiv p\pmod{q^2}$ and $q^p\equiv q \pmod{p^2}$ hold.

Externí odkaz: http://arxiv.org/abs/2010.05651

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Fermat's Last Theorem and Catalan's Conjecture in Weak Exponential Arithmetics

Autor: Glivický, Petr, Kala, Vítězslav

Publikováno v: Math. Log. Quart. 63 (2017), 162 - 174

We study Fermat's Last Theorem and Catalan's conjecture in the context of weak arithmetics with exponentiation. We deal with expansions (B,e) of models of arithmetical theories (in the language L=(0,1,+,x,<)) by a binary (partial or total) function e

Externí odkaz: http://arxiv.org/abs/1602.03580

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Akademický článek

Catalan's Conjecture

Autor: Ribenboim, Paulo

Publikováno v: The American Mathematical Monthly, 1996 Aug 01. 103(7), 529-538.

Externí odkaz: https://www.jstor.org/stable/2974663

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Catalan's Conjecture over Number Fields

Autor: Balasubramanian, R., Prakash, Pandey Prem

Catalan conjecture/Mihailescu theorem is a theorem in number theory that was conjectured by Mathematician Eugene Charles Catalan in 1844 and was proved completely by Preda Mihailescu in 2005. Some form of problem dates back atleast to Gersonides who

Externí odkaz: http://arxiv.org/abs/0901.4305

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