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%I #16 Sep 08 2022 08:46:24
%S 1,2,6,13,14,174,854,2694,78126,103973,106694,121974,420209,487374,
%T 1299374,2174654,3895094,4151454,5842214,5951129,6508334,10637054,
%U 20117894,24482957,31999694,32282053,32620202,32872454,34258454,52657397,56114618,57679082,65538437,70782774,71899526
%N Numbers m that divide 5^(m + 1) + 1.
%C Conjecture: For k > 1, k^(m + 1) == -1 (mod m) has an infinite number of positive solutions.
%t Select[Range[719*10^5],PowerMod[5,#+1,#]==#-1&] (* _Harvey P. Dale_, Jul 03 2020 *)
%o (Magma) [n + 1: n in [0..2000000] | Modexp(5, n + 2, n + 1) eq n];
%o (PARI) isok(m) = Mod(5, m)^(m+1) == -1; \\ _Jinyuan Wang_, Nov 16 2019
%Y Cf. A055685.
%Y Solutions to k^(m + 1) == -1 (mod m): A296369 (k=2), A328230 (k=3), A329168 (k=4), this sequence (k=5), A329226 (k=6).
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Nov 08 2019