Vipul at 20:01, 20 April 2009

2009-04-20T20:01:35Z

← Older revision		Revision as of 20:01, 20 April 2009
Line 2:		Line 2:

	A '''composite Fermat number''' is a [[Fermat number]] that is also a composite number, i.e., it is not a Fermat prime.		A '''composite Fermat number''' is a [[Fermat number]] that is also a composite number, i.e., it is not a Fermat prime.

			==Facts==

			===Constraints on prime divisors===

			{{further\|[[Prime divisor of Fermat number is congruent to one modulo large power of two]]}}

			If <math>k \ge 3</math>, and <math>F_k</math> is a composite Fermat number, then <math>2^{k+2}</math> divides <math>p - 1</math> for any prime divisor <math>p</math> of <math>F_k</math>. As a corollary, <math>2^{k+2}</math> divides <math>m-1</math> for ''any'' divisor <math>m</math> of <math>F_k</math>.

	==Relation with other properties==		==Relation with other properties==

Vipul: Created page with '==Definition== A '''composite Fermat number''' is a Fermat number that is also a composite number, i.e., it is not a Fermat prime. ==Relation with other properties== ===We...'

2009-04-20T19:58:46Z

Created page with '==Definition== A '''composite Fermat number''' is a Fermat number that is also a composite number, i.e., it is not a Fermat prime. ==Relation with other properties== ===We...'

New page

==Definition==

A '''composite Fermat number''' is a [[Fermat number]] that is also a composite number, i.e., it is not a Fermat prime.

==Relation with other properties==

===Weaker properties===

* [[Stronger than::Composite Proth number]]
* [[Stronger than::Poulet number]]: It is a [[Fermat pseudoprime]] to the base <math>2</math>.
* [[Strong pseudoprime]] to base <math>2</math>.

Composite Fermat number - Revision history

Vipul at 20:01, 20 April 2009

Vipul: Created page with '==Definition== A '''composite Fermat number''' is a Fermat number that is also a composite number, i.e., it is not a Fermat prime. ==Relation with other properties== ===We...'