Search: id:A039678
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%I A039678
%S A039678 5,8,7,18,3,19,38,28,28,14,115,18,51,19,53,338,53,264,143,11,306,31,99,
%T A039678 184,53,181,43,164,96,68,38,58,19,328,313,78,226,65,253,259,532,78,176,
%U A039678 276,143,174,165,69,330,44,33,332,94,263,48,79,171,747,731,20,147,91,40
%N A039678 Smallest a>1 such that a^(p-1)-1 is divisible by p^2, p = n-th prime.
%C A039678 Using Fermat's little theorem twice, it is easy to see that a=p^2-1 solves 
               this problem for all odd primes p. In fact, there appear to be exactly 
               p-1 values of a with 1 <= a <= p^2 for which a^(p-1)=1 (mod p^2). 
               See A096082 for the related open problem. - T. D. Noe (noe(AT)sspectra.com), 
               Aug 24 2008
%D A039678 P. Ribenboim, The New Book of Prime Number Records, Springer, 1996, 345-349.
%H A039678 T. D. Noe, <a href="b039678.txt">Table of n, a(n) for n = 1..10000</a>
%e A039678 For n=3, p=5 is 3rd prime and 5^2 = 25 divides 7^4 - 1 = 2401.
%Y A039678 Sequence in context: A165909 A019845 A053787 this_sequence A131040 A007450 
               A155735
%Y A039678 Adjacent sequences: A039675 A039676 A039677 this_sequence A039679 A039680 
               A039681
%K A039678 nonn,nice
%O A039678 1,1
%A A039678 Felice Russo (felice.russo(AT)katamail.com)
%E A039678 More terms from David W. Wilson (davidwwilson(AT)comcast.net)

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