Fermat pseudoprime - Revision history

Vipul at 21:36, 3 January 2012

2012-01-03T21:36:32Z

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	In other words, <math>n</math> divides <math>a^{n-1} - 1</math>, or, the order of <math>a</math> mod <math>n</math> divides <math>n - 1</math>.		In other words, <math>n</math> divides <math>a^{n-1} - 1</math>, or, the order of <math>a</math> mod <math>n</math> divides <math>n - 1</math>.

			==Facts==

			* [[Formula for number of bases to which a number is a Fermat pseudoprime]]
	==Relation with other properties==		==Relation with other properties==

Vipul: /* Property when applied to one or more choice of base */

2009-04-19T22:28:08Z

Property when applied to one or more choice of base

← Older revision		Revision as of 22:28, 19 April 2009
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	===Property when applied to one or more choice of base===		===Property when applied to one or more choice of base===

	* [[~~Absolute pseudoprime~~]] is a number that is a Fermat pseudoprime for every (relatively prime) base.		* [[Carmichael number]] is a number that is a Fermat pseudoprime for every (relatively prime) base.
	* [[Poulet number]] is a Fermat pseudoprime to base <math>2</math> (in particular, it needs to be an odd number).		* [[Poulet number]] is a Fermat pseudoprime to base <math>2</math> (in particular, it needs to be an odd number).

Vipul at 22:27, 19 April 2009

2009-04-19T22:27:20Z

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	{{base-relative pseudoprimality property}}		{{base-relative pseudoprimality property}}
	{{nottobeconfusedwith\|Fermat prime}}		{{nottobeconfusedwith\|[[Fermat prime]]}}
	==Definition==		==Definition==

Vipul at 22:26, 19 April 2009

2009-04-19T22:26:41Z

← Older revision		Revision as of 22:26, 19 April 2009
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	{{base-relative pseudoprimality property}}		{{base-relative pseudoprimality property}}
			{{nottobeconfusedwith\|Fermat prime}}
	==Definition==		==Definition==

Vipul: Created page with '{{base-relative pseudoprimality property}} ==Definition== Suppose $n$ is a composite natural number and $a$ is relatively prime to $n$ . $n...'$

2009-03-21T23:03:01Z

Created page with '{{base-relative pseudoprimality property}} ==Definition== Suppose <math>n</math> is a composite natural number and <math>a</math> is relatively prime to <math>n</math>. <math>n...'

New page

{{base-relative pseudoprimality property}}

==Definition==

Suppose <math>n</math> is a composite natural number and <math>a</math> is relatively prime to <math>n</math>. <math>n</math> is termed a '''Fermat pseudoprime''' relative to base <math>a</math> if we have:

<math>a^{n-1} \equiv 1 \mod n</math>.

In other words, <math>n</math> divides <math>a^{n-1} - 1</math>, or, the order of <math>a</math> mod <math>n</math> divides <math>n - 1</math>.

==Relation with other properties==

===Stronger properties===

* [[Weaker than::Strong pseudoprime]] to a given base.
* [[Weaker than::Euler pseudoprime]] to a given base.
* [[Weaker than::Euler-Jacobi pseudoprime]] to a given base.

===Property when applied to one or more choice of base===

* [[Absolute pseudoprime]] is a number that is a Fermat pseudoprime for every (relatively prime) base.
* [[Poulet number]] is a Fermat pseudoprime to base <math>2</math> (in particular, it needs to be an odd number).

Fermat pseudoprime - Revision history

Vipul at 21:36, 3 January 2012

Vipul: /* Property when applied to one or more choice of base */

Vipul at 22:27, 19 April 2009

Vipul at 22:26, 19 April 2009

Vipul: Created page with '{{base-relative pseudoprimality property}} ==Definition== Suppose n is a composite natural number and a is relatively prime to n. n...'

Vipul: Created page with '{{base-relative pseudoprimality property}} ==Definition== Suppose $n$ is a composite natural number and $a$ is relatively prime to $n$ . $n...'$