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there is no rule that "conjecture" gets replaced by "theorem" and there certainly is no rule that says that since
Mihailescu proved the Catalan conjecture, it becomes "Mihailescu's theorem". If indeed it is known as that, then it is for societal reasons which are murky. In fact, I kind of doubt that so famous a conjecture as this would be renamed so quickly (if ever). "Mihailescu's theorem" in Google Scholar brings up only a handful of hits. I propose this page be moved back to "Catalan conjecture" unless it can be demonstrated that "Mihailescu's theorem" is the common name for this now. --
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289:, but a quick reading of that article doesn't make any reference to such a claim. And googling "Chudnowski" just turns up a number of clones of this article. It seems to me that the statement "though Chudnowski has claimed to prove it" needs to be removed, unless someone can come up with a source for it.—
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Naming isn't that simple. The name of a theorem, even if it used to be a conjecture, is largely based on societal factors. The Smith conjecture (proven for over 20 years now), is still called the "Smith conjecture", and Fermat's Last
Theorem didn't become called "Wiles' theorem". To put it simply,
181:, my reply is that "consecutive" makes no sense in those contexts, and indeed it's standard to interpret "consecutive number" in the context of natural numbers (or integers), unless otherwise specified. —
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Many entries in the table appear to be erroneous. For example, 250000 (distance 47, allegedly) is not a perfect power. It has 2 and 5 as factors. I tried to check several entries unsuccessfully.
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At least the first sentence "Catalan's conjecture is a simple conjecture in number theory..." should be "Catalan's conjecture is a simple theorem in number theory...", shouldn't it? -
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If n and n+1 are both perfect powers, then n = 8. Another conjecture is: if n is a natural number and n+n+1 is a perfect power, then n = 18, is it true? More generally, if
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that 26 is the only number between a square (25) and a cube (27), and that it would seem that 26 is the only number between two powers. He has verified this up to 10^7. --
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Noticing that nobody ever made the move nor commented against it, I have made the move back and cleaned up the self-references within the article.--
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How is Pillai's conjecture the same as
Mihailescu's theorem? I will change the link after a week if no one gives me an answer.
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The only source for this article is to a non-online reference. Can anyone provide something clickable and checkable?
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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I support the above argument, and very strongly suggest that the page be moved back to "Catalan conjecture".
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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So shouldn't this page be moved to "Catalan's theorem" since it's been proven? --
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The unsourced parenthetical statement in this article might refer to one of the
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What does 'exp' mean in this context? Is it ], as in e^(e^(e^(e^730))))Â ?
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On Feb. 11h, 2010 Alonso Del Arte stated on <seqfan@list.seqfan.eu: -->
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though
Chudnowski has claimed to prove it (Pillai's conjecture)
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What is meant by "d is the difference of a perfect power n"?--
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for additional information. I made the following changes:
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