Proof needed

[Richard Guy]

A fourth power is congruent to 1 mod 5, unless it is
already a multiple of 5.  A square is congruene to 1
mod 3 unless it's already a mult of 3.  Similarly for
a sixth power mod 7 and a twelfth power mod 13.
This is Fermat's little theorem.   R.

On Sun, 31 Dec 2006, Artur wrote:

> Much more all these numbers are divisable by 3*5*7*13=1365
>
> Dnia 31-12-2006 o 17:20:30 Artur <grafix at csl.pl> napisa?(a):
>
>> 
>> Dear Seqfans,
>> Is possible to find number n that n^12+4094 is prime and n mod 5 isn't 0
>> if not how to proof these ???
>> 
>> 170625, 181545, 233415, 490035, 492765, 552825, 591045, 642915, 885885, \
>> 921375, 1262625, 1358175, 1481025, 1743105, 1748565, 1901445, 2029755, \
>> 2062515, 2073435, 2119845, 2193555, 2302755, 2532075, 2761395, 2764125, \
>> 2772315, 3012555, 3083535, 3258255, 3405675, 3648645, 3752385, 3891615, \
>> 4036305, 4172805, 4186455, 4437615, 4464915, 4473105, 4579575, 4642365, \
>> 4912635, 5051865, 5136495, 5163795, 5578755, 5625165, 5794425, 5960955, \
>> 5985525, 6124755, 6187545, 6255795, 6403215, 6405945, 6419595, 6736275, \
>> 6987435, 7006545, 7164885, 7197645, 7320495, 7386015, 7522515, 7710885, \
>> 7869225, 7972965, 8019375, 8090355, 8707335, 8748285, 8778315, 8797425, \
>> 8857485, 8917545, 9037665, 9084075, 9097725, 9168705, 9171435, 9329775, \
>> 9477195, 9482655, 9564555, 9570015, 9651915, 9671025, 9698325, 9739275, \
>> 9752925
>> 
>> %S A126894 170625, 181545, 233415, 490035, 492765, 552825, 591045, 642915, 
>> 885885, 921375
>> %N A126894 Numbers n such that n^12+4094 is prime.
>> %D A126894 Ribenboim P., 1996. The Little Book of Big Primes. Spriner 
>> Verlag.
>> %t A126894 a = {}; Do[If[PrimeQ[x^12 + 4094], AppendTo[a, x]], {x, 170624, 
>> 1000000}]; a
>> %Y A126894 A066386, A126893, A126895
>> %O A126894 1
>> %K A126894 ,nonn,
>> %A A126894 Artur Jasinki (grafix at csl.pl), Dec 31 2006
>> 
>> 
>> __________ NOD32 Informacje 1949 (20061230) __________
>> 
>> Wiadomosc zostala sprawdzona przez System Antywirusowy NOD32
>> http://www.nod32.com lub http://www.nod32.pl
>> 
>