A329222 Numbers m that divide 5^(m + 1) + 1.

1, 2, 6, 13, 14, 174, 854, 2694, 78126, 103973, 106694, 121974, 420209, 487374, 1299374, 2174654, 3895094, 4151454, 5842214, 5951129, 6508334, 10637054, 20117894, 24482957, 31999694, 32282053, 32620202, 32872454, 34258454, 52657397, 56114618, 57679082, 65538437, 70782774, 71899526

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..35.

Mathematica

Select[Range[719*10^5], PowerMod[5, #+1, #]==#-1&] (* Harvey P. Dale, Jul 03 2020 *)

Prog

(Magma) [n + 1: n in [0..2000000] | Modexp(5, n + 2, n + 1) eq n];
(PARI) isok(m) = Mod(5, 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), this sequence (k=5), A329226 (k=6).

Sequence in context: A130533 A231384 A082722 * A030416 A353588 A353971

Adjacent sequences: A329219 A329220 A329221 * A329223 A329224 A329225

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 08 2019

Status

approved