A327468 Numbers m that divide 8^m + 7.

1, 3, 5, 25, 519, 290502305, 821808425, 979288025, 982989263, 25783323897, 27771237541, 31045665345, 65130752425, 3708883906025, 15079242289703, 973336048301405

Offset: 1

Author

Juri-Stepan Gerasimov, Oct 04 2019

Keywords

• nonn
• more

Comments

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

Integer m not divisible by 3 is a term if and only if 3m is a term of A240941. - Max Alekseyev, Feb 07 2024

Also terms 930486448009391617725 and 21036656390681764555645540794214294457925. - Giovanni Resta, Oct 04 2019

Other terms 71245661271703622047, 7093208961478946798805, 7807963392818324067361574236385. - Max Alekseyev, Feb 07 2024

Crossrefs

Solutions to k^m == 1-k (mod m): 1 (k = 1), A006521 (k = 2), A015973 (k = 3), A327840 (k = 4), A123047 (k = 5), A327943 (k = 6), A328033 (k = 7), this sequence (k = 8).

Cf. A240941, A253211.

Programs

Magma

[m: m in [1..7] | (8^m + 7) mod m eq 0] cat [m: m in [8..10^8] | Modexp(8, m, m) + 7 eq m]; // Jon E. Schoenfield, Oct 05 2019

PARI

isok(n) = Mod(8, n)^n==-7; \\ Michel Marcus, Oct 05 2019

Extensions

a(10)-a(13) from Giovanni Resta, Oct 04 2019

a(14)-a(16) from Max Alekseyev, Feb 07 2024