A128679 Numbers k such that k^3 divides 5^(k^2) + 1.

1, 3, 21, 609, 903, 2667, 9429, 15501, 18543, 26187, 77343, 108507, 114681, 159663, 212541, 273441, 318507, 405447, 537747, 797349, 1197483, 1357503, 1398747, 1731387, 2354961, 3146703, 3325749, 4451181, 4630227, 4665801, 5192943

Offset: 1

Author

Alexander Adamchuk, Mar 31 2007

Keywords

• hard
• nonn

Comments

3 divides a(n) for n > 1. 7 divides a(n) for n > 2.

Crossrefs

Cf. A127263 (numbers k such that k^3 divide 2^(k^2)+1).

Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).

Cf. A128678, A128680, A128681, A128682, A128683, A128684, A128685.

Programs

Mathematica

Select[Range[5*10^6], Mod[ 5^(#^2)+1, #^3]==0 &] (* G. C. Greubel, Jan 18 2018 *)

Extensions

More terms from Ryan Propper, Dec 31 2007