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*{{#vardefine:k|{{#explode:{{#arrayindex:GFNlist|{{#var:i}}}}|,|0}}}}<!--
 
*{{#vardefine:k|{{#explode:{{#arrayindex:GFNlist|{{#var:i}}}}|,|0}}}}<!--
-->{{#ifeq:{{Is Long number|{{#var:k}}}}|1|{{#vardefine:k|{{Long number:{{#var:k}}-NS}}}}}}<!--
+
-->{{#ifeq:{{Is Long number|{{#var:k}}}}|1|{{#vardefine:k|{{Long number:{{#var:k}}-NS}}({{Long number:{{#var:k}}-DI}})}}}}<!--
 
-->{{#vardefine:n|{{#explode:{{#explode:{{#arrayindex:GFNlist|{{#var:i}}}}|,|1}}|#|0}}}}<!--
 
-->{{#vardefine:n|{{#explode:{{#explode:{{#arrayindex:GFNlist|{{#var:i}}}}|,|1}}|#|0}}}}<!--
 
-->{{#vardefine:dat|}}<!--
 
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}}<!--
 
}}<!--
 
-->{{#ifexpr:{{#len:{{#var:dat}}}}>0|, found {{#explode:{{#var:dat}}|&#32;|0}} by&#32;}}{{Contribs|{{#explode:{{#var:dat}}|&#32;|1}}|}}
 
-->{{#ifexpr:{{#len:{{#var:dat}}}}>0|, found {{#explode:{{#var:dat}}|&#32;|0}} by&#32;}}{{Contribs|{{#explode:{{#var:dat}}|&#32;|1}}|}}
}}{{#ifeq:{{NAMESPACENUMBER}}|0|[[Category:Generalized Fermat number {{{GFNa}}} {{{GFNb}}}|#.....{{padleft:{{{GFNn}}}|5|0}}]]}}
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}}{{#ifeq:{{NAMESPACENUMBER}}|0|[[Category:Generalized Fermat number {{{GFNa}}} {{{GFNb}}} Nums]]}}
 
{{#if:{{#var:facts}}|
 
{{#if:{{#var:facts}}|
 
==Factorization==
 
==Factorization==
 
<span class="longline">{{#vardefine:facts|{{#sub:{{#var:facts}}|2}}}}{{#var:facts}}}}</span>
 
<span class="longline">{{#vardefine:facts|{{#sub:{{#var:facts}}|2}}}}{{#var:facts}}}}</span>
 
</includeonly>
 
</includeonly>

Latest revision as of 08:51, 16 September 2021

Description

Template Generalized Fermat number

Collect the data of a Generalized Fermat number a2n + b2n, for b=1 this is a Fermat number a2n + 1.

Prototype

{{Generalized Fermat number
|GFNa=
|GFNb=
|GFNn=
|GFNFDBid=
|GFNDigits=
|GFNFactors=
|GFNState=
|GFNRemarks=
}}

Parameters

If 'GFNa'+'GFNb' is even, the numbers are always divisible by 2 and so 2 is not given as factor here.

If 'GFNFDBid' is given, a link to the FactorDB is created, otherwise only the number in standard notation is given.

For the case (a,b) = (8,1) the number for Fn(8,1) div 22n+1 = 42n − 22n + 1 is given.

See also

Example

{{Generalized Fermat number
|GFNa=2
|GFNb=1
|GFNn=207
|GFNFDBid=1000000000002000017
|GFNDigits=1234
|GFNFactors=
3,5
3,209
7,14
15288227662166113,8
N1100000002618011261,9
P345
C1133,1100000000212123761
U12345,4545
|GFNState=CF
|GFNRemarks=test
}}

will create:

Current data

a b n : 2 1 207
FactorDB : ID: 1000000000002000017 / Formula: 22207+1
Digits : 1234
State : CF
Remarks :
test

Factors

Factorization

97 * 2468256835981809063232453773836025757474103798450369795022913537<64> * 114689 * 3913786281514524929<19> * 707275264749309881405141965802671548079179711820351316861777644606207216944972589404100097<90> * P<345> * C<1133> * U<12345>