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Positive integers n such that 13^n == 6 (mod n).
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%I #18 Apr 10 2020 22:10:32

%S 1,7,8743,50239,312389,8789977,87453889,96301009,3963715129,

%T 5062673539,6854133309107,16987071590111,72278468169733,

%U 411419589731633,590475819370933

%N Positive integers n such that 13^n == 6 (mod n).

%C No other terms below 10^15. A large term: 2455610470454186971078168169. - _Max Alekseyev_, Dec 19 2017

%t Join[{1}, Select[Range[1, 9000], Mod[13^#, #] == 6 &]] (* _G. C. Greubel_, Nov 19 2017 *)

%t Join[{1}, Select[Range[10000000], PowerMod[13, #, #] == 6 &]] (* _Robert Price_, Apr 10 2020 *)

%o (PARI) isok(n) = Mod(13, n)^n == 6; \\ _Michel Marcus_, Nov 19 2017

%Y Solutions to 13^n == k (mod n): A001022 (k=0), A015963 (k=-1), A116621 (k=1), A116622 (k=2), A116629 (k=3), A116630 (k=4), A116611 (k=5), this sequence (k=6), A116632 (k=7), A295532 (k=8), A116636 (k=9), A116620(k=10), A116638 (k=11), A116639 (k=15).

%Y Cf. A116609, A128122, A277628, A277350.

%K nonn

%O 1,2

%A _Zak Seidov_, Feb 19 2006

%E More terms from _Ryan Propper_, Mar 30 2007

%E Term 1 is prepended and a(11)-a(15) added by _Max Alekseyev_, Jun 29 2011, Dec 19 2017