Semigroup with two elements - Revision history

en>ShoobyD at 13:04, 11 December 2014

2014-12-11T13:04:06Z

← Older revision		Revision as of 15:04, 11 December 2014
Line 1:		Line 1:


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It ~~supports backup scheduling and allows you~~ to ~~either download the backup file~~ or ~~email it to you~~. ~~Fortunately, Word - Press Customization Service is available these days, right from custom theme design, to plugin customization and modifying your website,~~ you ~~can take any bespoke service for~~ your ~~Word - Press development project~~. <br><br>~~Under Settings —> Reading~~, ~~determine if posts or a static page will be your home page, and if your home page~~ is ~~a static page, what page will contain blog posts~~. ~~By using Word - Press MLM websites or blogs, an online presence for~~ you ~~and your MLM company~~ can be ~~created swiftly and simply. 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en>Krishnachandranvn at 14:12, 6 February 2014

2014-02-06T14:12:25Z

← Older revision		Revision as of 16:12, 6 February 2014
Line 1:		Line 1:
	~~In [[number theory]], the '''Fermat–Catalan conjecture''' combines ideas of [[Fermat's last theorem]] and the [[Catalan conjecture]], hence the name. The conjecture states that the equation~~
	~~{{NumBlk\|::\|<math>a^m + b^n = c^k\quad</math>\|{{EquationRef\|1}}}}~~
	has only finitely many solutions (''a'',''b'',''c'',''m'',''n'',''k'') with distinct triplets of values (''a''<sup>''m''</sup>, ''b''<sup>''n''</sup>, ''c''<sup>''k''</sup>); here ''a'', ''b'', ''c'' are positive [[coprime]] integers and ''m'', ''n'', ''k'' are positive integers satisfying
	~~{{NumBlk\|::\|<math>\frac{1}{m}+\frac{1}{n}+\frac{1}{k}<1.</math>\|{{EquationRef\|2}}}}~~

	As of 2008, the following solutions to (1) are known:<ref name=pcm>{{citation\|first=Carl\|last=Pomerance\|authorlink=Carl Pomerance\|contribution=Computational Number Theory\|pages=361–362\|title=[[The Princeton Companion to Mathematics]]\|editor1-first=Timothy\|editor1-last=Gowers\|editor1-link=Timothy Gowers\|editor2-first=June\|editor2-last=Barrow-Green\|editor3-first=Imre\|editor3-last=Leader\|editor3-link=Imre Leader\|year=2008\|publisher=Princeton University Press\|isbn=978-0-691-11880-2}}.</ref>

	:<~~math~~>~~1^m+2^3=3^2\;~~<~~/math~~>		They're always ready to help, and they're always making changes to the site to make sure you won't have troubles in the first place. Medical word press themes give you the latest medical designs. Wordpress Content management systems, being customer friendly, can be used extensively to write and manage websites and blogs. Word - Press also provides protection against spamming, as security is a measure issue. It's as simple as hiring a Wordpress plugin developer or learning how to create what is needed. <br><br>Most Word - Press web developers can provide quality CMS website solutions and they price their services at reasonable rates. WPTouch is among the more well known Word - Press smartphone plugins which is currently in use by thousands of users. This may possibly also permit it currently being seriously straightforward to modify the hues within your Ad - Sense code so the ads blend nicely with the many term broad internet word wide web web page in case you can come to your conclusion to run the adverts. E-commerce websites are meant to be buzzed with fresh contents, graphical enhancements, and functionalities. By using Word - Press, you can develop very rich, user-friendly and full-functional website. <br><br>ve labored so hard to publish and put up on their website. Now if we talk about them one by one then -wordpress blog customization means customization of your blog such as installation of wordpress on your server by wordpress developer which will help you to acquire the SEO friendly blog application integrated with your site design as well as separate blog administration panel for starting up your own business blog,which demands a experienced wordpress designer. Possibly the most downloaded Word - Press plugin, the Google XML Sitemaps plugin but not only automatically creates a site map linking to everyone your pages and posts, it also notifies Google, Bing, Yahoo, and Ask. If you liked this post and you would such as to receive more details concerning [http://www.shortlinki.com/wordpress_dropbox_backup_2173312 wordpress backup plugin] kindly check out our web-page. Storing write-ups in advance would have to be neccessary with the auto blogs. Purchase these from our site, or bring your own, it doesn't matter, we will still give you free installation and configuration. <br><br>The primary differences are in the plugins that I install, as all sites don't need all the normal plugins. Cameras with a pentaprism (as in comparison to pentamirror) ensure that little mild is lost before it strikes your eye, however these often increase the cost of the digital camera considerably. Enterprise, when they plan to hire Word - Press developer resources still PHP, My - SQL and watch with great expertise in codebase. It supports backup scheduling and allows you to either download the backup file or email it to you. Fortunately, Word - Press Customization Service is available these days, right from custom theme design, to plugin customization and modifying your website, you can take any bespoke service for your Word - Press development project. <br><br>Under Settings —> Reading, determine if posts or a static page will be your home page, and if your home page is a static page, what page will contain blog posts. By using Word - Press MLM websites or blogs, an online presence for you and your MLM company can be created swiftly and simply. Must being, it's beneficial because I don't know about you, but loading an old website on a mobile, having to scroll down, up, and sideways' I find links being clicked and bounced around like I'm on a freaking trampoline. Word - Press is the most popular personal publishing platform which was launched in 2003. Verify whether your company has a team of developers or programmers having hands-on experience and knowledge about all Word - Press concepts.
	:<~~math~~>~~2^5+7^2=3^4\;~~<~~/math~~>
	:~~<math>13^2+7^3=2^9\;<~~/~~math>~~
	~~:<math>2^7+17^3=71^2\;<~~/~~math>~~
	~~:<math>3^5+11^4=122^2\;<~~/~~math>~~
	:<~~math~~>~~33^8+1549034^2=15613^3\;~~<~~/math>~~
	~~:<math>1414^3+2213459^2=65^7\;</math~~>
	~~:<math>9262^3+15312283^2=113^7\;</math>~~
	~~:<math>17^7+76271^3=21063928^2\;</math>~~
	~~:<math>43^8+96222^3=30042907^2\;</math>~~

	The ~~first of these~~ (~~1<sup>''m''</sup>+2<sup>3</sup>=3<sup>2</sup>~~) is the ~~only solution where one~~ of ~~''a''~~, ~~''b''~~ or ~~''c''~~ is 1, ~~according~~ to ~~the [[Catalan conjecture]]~~, ~~proven in 2002 by [[Preda Mihăilescu]]. While this case leads to infinitely many solutions of (1) (since we~~ can ~~pick~~ any ~~''m''~~ for ~~m>6), these solutions only give a single triplet of values (''a''~~<~~sup~~>~~''m''~~<~~/sup~~>~~, ''b''<sup>''n''</sup~~>, ~~''c''<sup>''k''</sup>).~~

	~~It is known by [[Faltings' theorem]] that for any fixed choice of positive integers ''m''~~, ~~''n''~~ and ~~''k'' satisfying (2)~~, ~~only finitely many coprime triples (''a''~~,~~ ''b''~~,~~ ''c~~''~~) solving (1) exist~~, but ~~of course the full Fermat–Catalan conjecture is~~ a ~~much stronger statement since it allows for an infinitude of sets of exponents ''m''~~, '~~'n''~~ and '~~'k''~~.

	~~The [[abc conjecture]] implies~~ the ~~Fermat–Catalan conjecture.<ref name=pcm/>~~

	~~[[Beal's conjecture]] is that all FCC solutions use 2 as an exponent~~.

	~~==See also==~~

	*[[Sums of powers]], a ~~list~~ of ~~related conjectures~~ and ~~theorems~~

	~~==References==~~
	~~{{reflist}}~~

	~~{{DEFAULTSORT:Fermat~~-~~Catalan conjecture}}~~
	~~[[Category:Conjectures]]~~
	~~[[Category:Number theory]]~~


	~~{{numtheory-stub}}~~

en>Quondum: /* The two-element semigroup ({0,1}, \wedge) */ mentioning "obvious" familiar example of multiplicative monoid

2013-10-06T20:35:50Z

The two-element semigroup ({0,1}, \wedge): mentioning "obvious" familiar example of multiplicative monoid

← Older revision		Revision as of 22:35, 6 October 2013
Line 1:		Line 1:
			In [[number theory]], the '''Fermat–Catalan conjecture''' combines ideas of [[Fermat's last theorem]] and the [[Catalan conjecture]], hence the name. The conjecture states that the equation
			{{NumBlk\|::\|<math>a^m + b^n = c^k\quad</math>\|{{EquationRef\|1}}}}
			has only finitely many solutions (''a'',''b'',''c'',''m'',''n'',''k'') with distinct triplets of values (''a''<sup>''m''</sup>, ''b''<sup>''n''</sup>, ''c''<sup>''k''</sup>); here ''a'', ''b'', ''c'' are positive [[coprime]] integers and ''m'', ''n'', ''k'' are positive integers satisfying
			{{NumBlk\|::\|<math>\frac{1}{m}+\frac{1}{n}+\frac{1}{k}<1.</math>\|{{EquationRef\|2}}}}

			As of 2008, the following solutions to (1) are known:<ref name=pcm>{{citation\|first=Carl\|last=Pomerance\|authorlink=Carl Pomerance\|contribution=Computational Number Theory\|pages=361–362\|title=[[The Princeton Companion to Mathematics]]\|editor1-first=Timothy\|editor1-last=Gowers\|editor1-link=Timothy Gowers\|editor2-first=June\|editor2-last=Barrow-Green\|editor3-first=Imre\|editor3-last=Leader\|editor3-link=Imre Leader\|year=2008\|publisher=Princeton University Press\|isbn=978-0-691-11880-2}}.</ref>

	~~Bonus~~: ~~WP Twin and WP Twin Auto Backup~~: (~~link to~~ ) ~~While not a theme, I think this software~~ is ~~essential if you are maintaining your Wordpress blog or regularly create new blog sites. You can either install Word - Press yourself or use free services offered on~~ the ~~web today. A pinch~~ of tablet centric strategy can get your Word - Press site miles ahead of your competitors, so here are few strategies that will give your Wordpress websites and blogs an edge over your competitors:. If you'~~re using Wordpress and want to make your blog~~ a ~~"dofollow" blog~~, ~~meaning that links from your blog pass on the benefits of Google pagerank, you can install one of the many dofollow plugins available. Understanding how Word - Press works can be a challenge, but it~~ is ~~not too difficult when you learn more about it. <br><br>Luckily~~, ~~for Word - Press users, WP Touch plugin transforms your site into an IPhone style theme. If you have any type of inquiries regarding where and~~ the ~~best ways to make use of~~ [~~http://scridle.nl/wordpress_dropbox_backup_51169 wordpress dropbox backup~~], ~~you can call us at the web page~~. ~~The higher your blog ranks on search engines, the more likely people will find your online marketing site. We also help~~ to ~~integrate various plug-ins to expand the functionalities~~ of ~~the web application. This is identical to doing a research as in depth above, nevertheless you~~ can ~~see various statistical details like the number of downloads and when the template was not long ago updated. Many times the camera is following Mia~~, ~~taking in her point~~ of ~~view in almost every frame.~~ <br><br>~~Saying that~~, ~~despite the launch of Wordpress Express many months ago~~, there has still been no sign of a Wordpress video tutorial on offer UNTIL NOW. After sending these details, your Word - Press blog will be setup within a few days. This platform can be customizedaccording to the requirements of the business. Newer programs allow website owners and internet marketers to automatically and dynamically change words in their content to match the keywords entered by their web visitors in their search queries'~~a feat that they cannot easily achieve with older software. After that the developer adds the unordered list for navigations.~~ <br><br>~~Word - Press has plenty of SEO benefits over Joomla and Drupal~~. ~~The SEOPressor Word - Press SEO Plugin works~~ by ~~analysing each page~~ and ~~post against your chosen keyword~~ (~~or keyword phrase~~) ~~and giving~~ a ~~score~~, ~~with instructions on how to improve~~ it~~. Exacting subjects in reality must be accumulated in head ahead~~ of ~~planning on your high quality theme~~. ~~Word - Press is the most popular open source content management system (CMS) in~~ the ~~world today. Digital digital cameras now function gray-scale configurations which allow expert photographers to catch images only in black and white~~. <br>~~<br>You will know which of your Word - Press blog posts are attracting more unique visitors which in turn will help you develop better products and services for your customers. Here~~'s a list of ~~some exciting Word~~ - ~~Press features that have created waves in the web development industry~~:~~. Word~~ - Press can also be quickly extended however improvement API is not as potent as Joomla's. with posts or testimonials updated as they are uploaded to a particular section of the website. Your topic is going to be the basis of your site's name.		:<math>1^m+2^3=3^2\;</math>
			:<math>2^5+7^2=3^4\;</math>
			:<math>13^2+7^3=2^9\;</math>
			:<math>2^7+17^3=71^2\;</math>
			:<math>3^5+11^4=122^2\;</math>
			:<math>33^8+1549034^2=15613^3\;</math>
			:<math>1414^3+2213459^2=65^7\;</math>
			:<math>9262^3+15312283^2=113^7\;</math>
			:<math>17^7+76271^3=21063928^2\;</math>
			:<math>43^8+96222^3=30042907^2\;</math>

			The first of these (1<sup>''m''</sup>+2<sup>3</sup>=3<sup>2</sup>) is the only solution where one of ''a'', ''b'' or ''c'' is 1, according to the [[Catalan conjecture]], proven in 2002 by [[Preda Mihăilescu]]. While this case leads to infinitely many solutions of (1) (since we can pick any ''m'' for m>6), these solutions only give a single triplet of values (''a''<sup>''m''</sup>, ''b''<sup>''n''</sup>, ''c''<sup>''k''</sup>).

			It is known by [[Faltings' theorem]] that for any fixed choice of positive integers ''m'', ''n'' and ''k'' satisfying (2), only finitely many coprime triples (''a'', ''b'', ''c'') solving (1) exist, but of course the full Fermat–Catalan conjecture is a much stronger statement since it allows for an infinitude of sets of exponents ''m'', ''n'' and ''k''.

			The [[abc conjecture]] implies the Fermat–Catalan conjecture.<ref name=pcm/>

			[[Beal's conjecture]] is that all FCC solutions use 2 as an exponent.

			==See also==

			*[[Sums of powers]], a list of related conjectures and theorems

			==References==
			{{reflist}}

			{{DEFAULTSORT:Fermat-Catalan conjecture}}
			[[Category:Conjectures]]
			[[Category:Number theory]]


			{{numtheory-stub}}

en>R'n'B: Fix links to disambiguation page True

2012-04-20T20:24:54Z

Fix links to disambiguation page True

New page

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