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

Author

Juri-Stepan Gerasimov, Oct 02 2019

Keywords

• nonn
• more

Comments

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

Also includes 2073273696480171732497. - Giovanni Resta, Oct 04 2019

Crossrefs

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).

Programs

Magma

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

Extensions

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

a(17) from Max Alekseyev, Feb 07 2024