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%I #37 Dec 10 2016 19:18:57
%S 2,3,4,6,8,12,15,16,20,24,30,32,40,48,51,60,64,68,80,96,102,120,128,
%T 136,160,192,204,240,255,256,272,320,340,384,408,480,510,512,544,640,
%U 680,768,771,816,960,1020,1024,1028,1088,1280,1360,1536,1542,1632,1920,2040
%N Numbers n with the property that in Z/nZ the equation x^y + 1 = 0 has only the trivial solutions with x == -1 (mod n).
%C It appears that odd terms 3, 15, 51, 255, 771, 3855, 13107, 65535, ... are given by A038192. - _Michel Marcus_, Aug 08 2013
%C This is the complement of A126949 in the numbers n > 1. (But it could be argued that the sequence should start with n = 1 as initial term.) It appears that for any a(k) in the sequence, 2*a(k) is also in the sequence. The primitive terms (not of the form a(k) = 2*a(m), m < k) are 2, 3, 15, 20, 51, 68, 255, 340, 771, 1028, .... (see A274003). - _M. F. Hasler_, Jun 06 2016
%H Arnaud Vernier and Charles R Greathouse IV, <a href="/A178751/b178751.txt">Table of n, a(n) for n = 1..189</a> (first 78 terms from Vernier)
%e In Z/3Z, the only solution to the equation x^y + 1 = 0 is x = 2 and y = 1. Whereas in Z/5Z, the equation has at least one nontrivial solution: 2^2 + 1 = 0.
%o (PARI) is(n)=for(x=2,n-2,if(gcd(x,n)>1,next);my(t=Mod(x,n));while(abs(centerlift(t))>1,t*=x);if(t==-1,return(0)));n>1 \\ _Charles R Greathouse IV_, Aug 08 2013
%Y Cf. A038192, A126949, A274003.
%K nonn
%O 1,1
%A _Arnaud Vernier_, Jun 09 2010, Jun 10 2010
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