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A178751 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). 4
2, 3, 4, 6, 8, 12, 15, 16, 20, 24, 30, 32, 40, 48, 51, 60, 64, 68, 80, 96, 102, 120, 128, 136, 160, 192, 204, 240, 255, 256, 272, 320, 340, 384, 408, 480, 510, 512, 544, 640, 680, 768, 771, 816, 960, 1020, 1024, 1028, 1088, 1280, 1360, 1536, 1542, 1632, 1920, 2040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It appears that odd terms 3, 15, 51, 255, 771, 3855, 13107, 65535, ... are given by A038192. - Michel Marcus, Aug 08 2013

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

LINKS

Arnaud Vernier and Charles R Greathouse IV, Table of n, a(n) for n = 1..189 (first 78 terms from Vernier)

EXAMPLE

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.

PROG

(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

CROSSREFS

Cf. A038192, A126949, A274003.

Sequence in context: A331088 A260653 A232711 * A309353 A081029 A300787

Adjacent sequences:  A178748 A178749 A178750 * A178752 A178753 A178754

KEYWORD

nonn

AUTHOR

Arnaud Vernier, Jun 09 2010, Jun 10 2010

STATUS

approved

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Last modified July 12 11:25 EDT 2020. Contains 335658 sequences. (Running on oeis4.)