1105 - Revision history

Vipul: /* Properties and families */

2012-01-03T21:17:13Z

Properties and families

← Older revision		Revision as of 21:17, 3 January 2012
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	\| [[satisfies property::Carmichael number]] (also called absolute pseudoprime) \|\| second Carmichael number \|\| {{#lst:Carmichael number\|list}} \|\| The [[universal exponent]] is <math>\operatorname{lcm} \{ 5-1,13-1,17-1 \} = 48</math> which divides 1105 - 1 = 1104.		\| [[satisfies property::Carmichael number]] (also called absolute pseudoprime) \|\| second Carmichael number \|\| {{#lst:Carmichael number\|list}} \|\| The [[universal exponent]] is <math>\operatorname{lcm} \{ 5-1,13-1,17-1 \} = 48</math> which divides 1105 - 1 = 1104.
	\|-		\|-
	\| [[satisfies property::Poulet number]] (also called Sarrus number) ([[Fermat pseudoprime]] to base 2) \|\| fourth Poulet number \|\| {{#lst:Poulet number\|list}} \|\| follows from its being ~~an odd~~ Carmichael number.		\| [[satisfies property::Poulet number]] (also called Sarrus number) ([[Fermat pseudoprime]] to base 2) \|\| fourth Poulet number \|\| {{#lst:Poulet number\|list}} \|\| follows from its being a Carmichael number (note that [[Carmichael number is odd]]).
	\|}		\|}

Vipul: /* Arithmetic functions */

2012-01-03T20:54:00Z

Arithmetic functions

← Older revision		Revision as of 20:54, 3 January 2012
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	\| {{arithmetic function value\|Euler totient function\|768}} \|\| The Euler totient function is <math>(5-1)(13-1)(17-1) = (4)(12)(16) = 768</math>.		\| {{arithmetic function value\|Euler totient function\|768}} \|\| The Euler totient function is <math>(5-1)(13-1)(17-1) = (4)(12)(16) = 768</math>.
	\|-		\|-
	\| {{arithmetic function value\|universal exponent\|48}} \|\| The universal exponent is <math>\operatorname{lcm}\{5-1,13-1,17-1\} = \~~operaotrname~~{lcm}\{4,12,16\} = 48</math>.		\| {{arithmetic function value\|universal exponent\|48}} \|\| The universal exponent is <math>\operatorname{lcm}\{5-1,13-1,17-1\} = \operatorname{lcm}\{4,12,16\} = 48</math>.
	\|-		\|-
	\| {{arithmetic function value\|Mobius function\|-1}} \|\| The number is a [[square-free number]] and it has an odd number of prime divisors (3 prime divisors)		\| {{arithmetic function value\|Mobius function\|-1}} \|\| The number is a [[square-free number]] and it has an odd number of prime divisors (3 prime divisors)

Vipul: /* Properties and families */

2012-01-03T20:53:38Z

Properties and families

@@ Line 12: / Line 12: @@
 {| class="sortable" border="1"
-! Property or family !! Parameter values !! First few numbers satisfying the property
+! Property or family !! Parameter values !! First few numbers satisfying the property !! Proof of satisfaction/containment/membership
 |-
-| [[satisfies property::Carmichael number]] (also called absolute pseudoprime) || second Carmichael number || {{#lst:Carmichael number|list}}
+| [[satisfies property::Carmichael number]] (also called absolute pseudoprime) || second Carmichael number || {{#lst:Carmichael number|list}} || The [[universal exponent]] is <math>\operatorname{lcm} \{ 5-1,13-1,17-1 \} = 48</math> which divides 1105 - 1 = 1104.
 |-
-| [[satisfies property::Poulet number]] (also called Sarrus number) ([[Fermat pseudoprime]] to base 2) || fourth Poulet number || {{#lst:Poulet number|list}}
+| [[satisfies property::Poulet number]] (also called Sarrus number) ([[Fermat pseudoprime]] to base 2) || fourth Poulet number || {{#lst:Poulet number|list}} || follows from its being an odd Carmichael number.
 |}

Vipul: Created page with "{{particular natural number}} ==Summary== ===Factorization=== 1105 is a square-free number. It has prime factors 5, 13, and 17: $\! 1105 = 5 * 13 * 17..."$

2012-01-03T20:49:13Z

Created page with "{{particular natural number}} ==Summary== ===Factorization=== 1105 is a square-free number. It has prime factors 5, 13, and 17: <math>\! 1105 = 5 * 13 * 17..."

New page

{{particular natural number}}

==Summary==

===Factorization===

1105 is a [[square-free number]]. It has prime factors [[5]], [[13]], and [[17]]:

<math>\! 1105 = 5 * 13 * 17</math>

===Properties and families===

{| class="sortable" border="1"
! Property or family !! Parameter values !! First few numbers satisfying the property
|-
| [[satisfies property::Carmichael number]] (also called absolute pseudoprime) || second Carmichael number || {{#lst:Carmichael number|list}}
|-
| [[satisfies property::Poulet number]] (also called Sarrus number) ([[Fermat pseudoprime]] to base 2) || fourth Poulet number || {{#lst:Poulet number|list}}
|}

1105 - Revision history

Vipul: /* Properties and families */

Vipul: /* Arithmetic functions */

Vipul: /* Properties and families */

Vipul: Created page with "{{particular natural number}} ==Summary== ===Factorization=== 1105 is a square-free number. It has prime factors 5, 13, and 17: \! 1105 = 5 * 13 * 17..."

Vipul: Created page with "{{particular natural number}} ==Summary== ===Factorization=== 1105 is a square-free number. It has prime factors 5, 13, and 17: $\! 1105 = 5 * 13 * 17..."$