A123052 Numbers k that divide 5^k + 3.

1, 2, 4, 14, 628, 11524, 16814, 188404, 441484, 2541014, 3984724, 172315684, 208268941, 40874725514, 280454588548, 489850370956, 1235856817732, 62479203805793, 95467808763364, 116016015619396, 396249210287836

Offset: 1

Author

Alexander Adamchuk, Nov 04 2006

Keywords

• hard
• nonn

Comments

No other terms below 10^15. A larger term: 783847656467936404. - Max Alekseyev, Oct 16 2016

Crossrefs

Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), A123062 (k=-2), A123061 (k=3), this sequence (k=-3), A125949 (k=4), A123047 (k=-4), A123091 (k=5), A015891 (k=-5), A277350 (k=6), A277348 (k=-6).

Programs

Mathematica

Select[Range[1000000], IntegerQ[(PowerMod[5,#,# ]+3)/# ]&]

PARI

is(n)=Mod(5,n)^n==-3 \\ Charles R Greathouse IV, Apr 06 2014

Extensions

a(10)-a(13) from Ryan Propper, Dec 30 2006, Jan 02 2007

More terms from Lars Blomberg, Nov 25 2011

Terms a(14) onwards were reported incorrect by Toshitaka Suzuki, and have been deleted. - N. J. A. Sloane, Mar 18 2014

a(14)-a(17) from Toshitaka Suzuki, Mar 18 2014, Apr 03 2014

a(18)-a(21) from Max Alekseyev, Oct 16 2016