A125949 Numbers k that divide 5^k - 4.

1, 4769, 8563651, 300414792131, 2353957351049, 15960089894129, 452045914836301, 657236915690111

Offset: 1

Author

Alexander Adamchuk, Feb 04 2007

Keywords

• hard
• more
• nonn

Comments

No other terms below 10^15. - Max Alekseyev, Oct 17 2016

Crossrefs

Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), A123062 (k=-2), A123061 (k=3), A123052 (k=-3), this sequence (k=4), A123047 (k=-4), A123091 (k=5), A015891 (k=-5), A277350 (k=6), A277348 (k=-6).

Programs

Mathematica

a(1) = 1; Do[ If[ PowerMod[5, 2n - 1, 2n - 1] - 4 == 0, Print[2n - 1]], {n,10^9}]

PARI

is(n)=Mod(5,n)^n==4 \\ Charles R Greathouse IV, May 15 2013

Extensions

a(4)-a(8) from Max Alekseyev, Jun 09 2010, Oct 17 2016