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A329226 Numbers m that divide 6^(m + 1) + 1. 1
1, 37, 16987849, 2416266949, 5995229029, 7193673829, 11465419549, 17783484529, 72155530501, 142013229529, 174523785589, 189282539137, 294183810997, 302690164297, 354613312129, 774557575609, 933821938789, 1407294504937, 1974020768389, 2112969494569, 2878251281401 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: For k > 1, k^(m + 1) == -1 (mod m) has an infinite number of positive solutions.

Terms cannot be a multiple of the following primes below 100: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43, 47, 53, 59, 67, 71, 79, 83. - Giovanni Resta, Nov 09 2019

LINKS

Table of n, a(n) for n=1..21.

PROG

(MAGMA) [n + 1: n in [0..20000000] | Modexp(6, n + 2, n + 1) eq n];

(PARI) isok(m) = Mod(6, m)^(m+1) == -1; \\ Jinyuan Wang, Nov 16 2019

CROSSREFS

Cf. A055685.

Solutions to k^(m + 1) == -1 (mod m): A296369 (k=2), A328230 (k=3), A329168 (k=4), A329222 (k=5).

Sequence in context: A289820 A087020 A238840 * A171407 A023930 A022072

Adjacent sequences:  A329223 A329224 A329225 * A329227 A329228 A329229

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Nov 08 2019

EXTENSIONS

a(5)-a(21) from Giovanni Resta, Nov 09 2019

STATUS

approved

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Last modified September 18 04:14 EDT 2020. Contains 337165 sequences. (Running on oeis4.)