A123062 Numbers k that divide 5^k + 2.

1, 7, 51373, 78127, 138943, 620299, 2842933, 137422693, 2259290321, 413879131637, 434757575329, 915535274009, 14864856896743

Offset: 1

Author

Alexander Adamchuk, Nov 04 2006

Keywords

• hard
• more
• nonn

Comments

No further terms up to 10^15. Larger term: 64629734103979763971. - Max Alekseyev, Oct 15 2016

Crossrefs

Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), this sequence (k=-2), A123061 (k=3), A123052 (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,#,# ]+2)/# ]&]

PARI

is(n)=Mod(5,n)^n==-2 \\ Charles R Greathouse IV, Nov 04 2016

Extensions

More terms from Farideh Firoozbakht, Nov 18 2006

a(9) from Ryan Propper, Jan 29 2007

a(10)-a(13) from Max Alekseyev, Jul 28 2009, Oct 15 2016