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A327468
Numbers m that divide 8^m + 7.
2
1, 3, 5, 25, 519, 290502305, 821808425, 979288025, 982989263, 25783323897, 27771237541, 31045665345, 65130752425, 3708883906025, 15079242289703, 973336048301405
OFFSET
1,2
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
PROG
(PARI) isok(n) = Mod(8, n)^n==-7; \\ Michel Marcus, Oct 05 2019
(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
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).
Sequence in context: A276968 A074701 A318179 * A140127 A226318 A154143
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(10)-a(13) from Giovanni Resta, Oct 04 2019
a(14)-a(16) from Max Alekseyev, Feb 07 2024
STATUS
approved