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A328138
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Numbers m divide 9^m + 8.
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0
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OFFSET
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1,2
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COMMENTS
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Conjecture: For n > 1, k^n == 1-k (mod n) has an infinite number of positive solutions.
a(6) > 10^12. No term can be a multiple of 2, 3, 5, 7, or 13. Also terms: 228454543831049 and 4879573990210017348077958628152400091281634488825721395187. - Giovanni Resta, Oct 07 2019
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LINKS
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Table of n, a(n) for n=1..5.
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PROG
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(MAGMA) [1] cat [n: n in [1..10^8] | Modexp(9, n, n) + 8 eq n];
(PARI) isok(n) = Mod(9, n)^n==-8; \\ Michel Marcus, Oct 05 2019
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CROSSREFS
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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).
Sequence in context: A308490 A249459 A191963 * A351181 A351769 A139091
Adjacent sequences: A328135 A328136 A328137 * A328139 A328140 A328141
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KEYWORD
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nonn,more
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AUTHOR
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Juri-Stepan Gerasimov, Oct 04 2019
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STATUS
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approved
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