Artin's conjecture on primitive roots - Revision history

Vipul: /* Relation with other conjectures and known facts */

2012-01-02T04:24:28Z

Relation with other conjectures and known facts

← Older revision		Revision as of 04:24, 2 January 2012
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	{{fillin}}		{{fillin}}
	==Relation with other conjectures and known facts==		==Relation with other conjectures and known facts==

			<section begin="related"/>

	{\| class="sortable" border="1"		{\| class="sortable" border="1"
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	\| [[Heath-Brown theorem on Artin's conjecture]] \|\| Artin's conjecture holds for all but two exceptional values of <math>a</math>. However, no explicit information about the explicit values of <math>a</math> \|\| Unconditional		\| [[Heath-Brown theorem on Artin's conjecture]] \|\| Artin's conjecture holds for all but two exceptional values of <math>a</math>. However, no explicit information about the explicit values of <math>a</math> \|\| Unconditional
	\|}		\|}
			<section end="related"/>

	==External links==		==External links==

	* [http://guests.mpim-bonn.mpg.de/moree/surva.pdf A survey of Artin's conjecture and the developments related to it (PDF)]		* [http://guests.mpim-bonn.mpg.de/moree/surva.pdf A survey of Artin's conjecture and the developments related to it (PDF)]

Vipul at 22:36, 29 May 2010

2010-05-29T22:36:15Z

← Older revision		Revision as of 22:36, 29 May 2010
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	\| [[Heath-Brown theorem on Artin's conjecture]] \|\| Artin's conjecture holds for all but two exceptional values of <math>a</math>. However, no explicit information about the explicit values of <math>a</math> \|\| Unconditional		\| [[Heath-Brown theorem on Artin's conjecture]] \|\| Artin's conjecture holds for all but two exceptional values of <math>a</math>. However, no explicit information about the explicit values of <math>a</math> \|\| Unconditional
	\|}		\|}

			==External links==

			* [http://guests.mpim-bonn.mpg.de/moree/surva.pdf A survey of Artin's conjecture and the developments related to it (PDF)]

Vipul: /* Relation with other conjectures and known facts */

2010-05-29T22:30:33Z

Relation with other conjectures and known facts

← Older revision		Revision as of 22:30, 29 May 2010
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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	\| Name of conjecture/fact !! Statement !! Conditional to ...		! Name of conjecture/fact !! Statement !! Conditional to ...
	\|-		\|-
	\| [[Hooley's theorem]] \|\| Artin's conjecture holds for all <math>a</math> \|\| (special cases of) [[weaker than::generalized Riemann hypothesis]]		\| [[Hooley's theorem]] \|\| Artin's conjecture holds for all <math>a</math> \|\| (special cases of) [[weaker than::generalized Riemann hypothesis]]

Vipul at 22:30, 29 May 2010

2010-05-29T22:30:05Z

@@ Line 3: / Line 3: @@
 ===Infinitude version===
-Suppose <math>a</math> is an integer that is not equal to <math>-1</math> and is not a [[perfect square]], i.e., <math>a</math> is not the square of an integer. Then, there exist infinitely many primes <math>p</math> such that <math>a</math> is a [[primitive root]] modulo <math>p</math>.
+Suppose <math>a</math> is an integer that is not equal to <math>-1</math> and is not a [[perfect square]], i.e., <math>a</math> is not the square of an integer. Then, there exist infinitely many primes <math>p</math> such that <math>a</math> is a [[fact about::primitive root]] modulo <math>p</math>.
-==Density version===
+===Density version===

Vipul: Created page with '==Statement== ===Infinitude version=== Suppose $a$ is an integer that is not equal to $-1$ and is not a perfect square, i.e., $a$ is not th...'

2009-04-19T23:30:09Z

Created page with '==Statement== ===Infinitude version=== Suppose <math>a</math> is an integer that is not equal to <math>-1</math> and is not a perfect square, i.e., <math>a</math> is not th...'

New page

==Statement==

===Infinitude version===

Suppose <math>a</math> is an integer that is not equal to <math>-1</math> and is not a [[perfect square]], i.e., <math>a</math> is not the square of an integer. Then, there exist infinitely many primes <math>p</math> such that <math>a</math> is a [[primitive root]] modulo <math>p</math>.

==Density version===

Artin's conjecture on primitive roots - Revision history

Vipul: /* Relation with other conjectures and known facts */

Vipul at 22:36, 29 May 2010

Vipul: /* Relation with other conjectures and known facts */

Vipul at 22:30, 29 May 2010

Vipul: Created page with '==Statement== ===Infinitude version=== Suppose a is an integer that is not equal to -1 and is not a perfect square, i.e., a is not th...'

Vipul: Created page with '==Statement== ===Infinitude version=== Suppose $a$ is an integer that is not equal to $-1$ and is not a perfect square, i.e., $a$ is not th...'