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A329226 Numbers m that divide 6^(m + 1) + 1. 1

%I #13 Sep 08 2022 08:46:24

%S 1,37,16987849,2416266949,5995229029,7193673829,11465419549,

%T 17783484529,72155530501,142013229529,174523785589,189282539137,

%U 294183810997,302690164297,354613312129,774557575609,933821938789,1407294504937,1974020768389,2112969494569,2878251281401

%N Numbers m that divide 6^(m + 1) + 1.

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

%C 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

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

%o (PARI) isok(m) = Mod(6, 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), A329222 (k=5).

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Nov 08 2019

%E a(5)-a(21) from _Giovanni Resta_, Nov 09 2019

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)