Toscead betweox fadungum "Fermat tæl"

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In [[rīmcræft]]um, '''Fermat tæl''', ȝenemnodgenemnod æfter [[Pierre de Fermat]], þǣm þe hīe ærest hogde, is [[positif tæl]] mid scape:
 
:<math>F_{n} = 2^{2^n} + 1</math>
:''F''<sub>7</sub> = 2<sup>128</sup> + 1 = 340282366920936963463374207431698420457 = 59694209133797217 × 5704680085685129054201
 
ȜifGif 2<sup>''n''</sup> + 1 [[frumtæl]] is, man cynþ ācȳðan þæt ''n'' must bēon 2-miht. (ȜifGif ''n'' = ''ab'' þæt 1 < ''a'', ''b'' < ''n'' and ''b'' is ofertæl, man hæfþ 2<sup>''n''</sup> + 1 ≡ (2<sup>''a''</sup>)<sup>''b''</sup> + 1 ≡ (−1)<sup>''b''</sup> + 1 ≡ 0 ('''mod''' 2<sup>''a''</sup> + 1).)
 
For þǣm ǣlc frumtæl mid scape 2<sup>''n''</sup> + 1 is Fermat tæl, and þās frumtalu hātte '''Fermat frumtalu'''. Man ƿātwāt ǣnlīce fīf Fermat frumtalu: ''F''<sub>0</sub>, ... ,''F''<sub>4</sub>.
 
== Basic properties ==
==Primality of Fermat numbers==
 
Fermat numbers ȝege Fermat primes ƿurdonwurdon ǣrest ȝehogodgehogod fram Pierre de Fermat, se þe [[rǽswung|rǣsƿoderǣswode]] þæt ealla Fermat rīma sind prime. Indeed, þā forman fīf Fermat rīma ''F''<sub>0</sub>,...,''F''<sub>4</sub> sind éaþtǽcne tó béonne (irregular) prime. Hwæðere wearþ þéos rǽswung onsacen fram [[Leonhard Euler]]e in 1732 mid þǽm þe hé cýðde þæt
 
:<math> F_{5} = 2^{2^5} + 1 = 2^{32} + 1 = 4294967297 = 641 \cdot 6700417 \; </math>
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