A327468 -id:A327468 - cp's OEIS frontend

A328033 Numbers m that divide 7^m + 6.

1, 13, 793, 1943, 150341, 183793, 2348789, 26052527, 27982637, 54789869, 1588344433, 3928538029, 8115802931, 16936276919, 17786709541, 47778790033, 973094452518029

Offset: 1

Juri-Stepan Gerasimov, Oct 02 2019

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

Also includes 2073273696480171732497. - Giovanni Resta, Oct 04 2019

Solutions to k^m == 1-k (mod m): A006521 (k = 2), A015973 (k = 3), A327840 (k = 4), A123047 (k = 5), A327943 (k = 6), this sequence (k = 7), A327468 (k = 8).

Cf. A253210 (7^n + 6).

[1] cat [n: n in [1..10^8] | Modexp(7, n, n) + 6 eq n];

a(12)-a(16) from Giovanni Resta, Oct 04 2019

a(17) from Max Alekseyev, Feb 07 2024

A328138 Numbers m that divide 9^m + 8.

Original entry on oeis.org

1, 17, 803, 1241, 20264753, 28214180783393, 228454543831049

Offset: 1

Juri-Stepan Gerasimov, Oct 04 2019

Conjecture: For n > 1, k^n == 1-k (mod n) has an infinite number of positive solutions.
No term can be a multiple of 2, 3, 5, 7, or 13. Also 4879573990210017348077958628152400091281634488825721395187 is a term. - Giovanni Resta, Oct 07 2019
Also 6788776064693081883870036833 is a term. - Max Alekseyev, Dec 27 2024

Subsequence of A008364.
Solutions to k^m == k-1 (mod m): 1 (k = 1), A006521 (k = 2), A015973 (k = 3), A327840 (k = 4), A123047 (k = 5), A327943 (k = 6), A328033 (k = 7), A327468 (k = 8), this sequence (k = 9).
Cf. A253212 (9^n + 8).

[1] cat [n: n in [1..10^8] | Modexp(9, n, n) + 8 eq n];

isok(n) = Mod(9, n)^n==-8; \\ Michel Marcus, Oct 05 2019

a(n) > 15n for large enough n. (Surely the sequence grows superlinearly, but I can't prove it.) - Charles R Greathouse IV, Dec 27 2024

a(7) from Giovanni Resta confirmed and a(6) added by Max Alekseyev, Dec 27 2024

cp's OEIS Frontend

A328033 Numbers m that divide 7^m + 6.

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