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).

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

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: A336508 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