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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

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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