A327943 Numbers m that divide 6^m + 5.

1, 11, 341, 186787, 8607491, 9791567, 11703131, 14320387, 50168819, 952168003, 71654478989, 1328490399527

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 30 2019

Keywords

• nonn
• more

Comments

Conjecture: For k > 1, k^m == 1 - k (mod m) has infinitely many positive solutions.

Also includes 11834972807906571233 = 31*381773316384082943. - Robert Israel, Oct 03 2019

a(13) > 10^15. - Max Alekseyev, Nov 10 2022

Crossrefs

Solutions to k^m == 1-k (mod m): A006521 (k = 2), A015973 (k = 3), A327840 (k = 4), A123047 (k = 5), this sequence (k = 6).

Cf. A245318, A277288, A015891, A253209.

Programs

Magma

[1] cat [n: n in [1..10^8] | Modexp(6, n, n) + 5 eq n];

Mathematica

Join[{1},Select[Range[98*10^5],PowerMod[6,#,#]==#-5&]] (* The program generates the first six terms of the sequence. To generate more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Feb 05 2022 *)

Extensions

a(11) from Giovanni Resta, Oct 02 2019

a(12) from Max Alekseyev, Nov 10 2022