A127105 Numbers k such that k^2 divides 5^k-1.

1, 2, 4, 6, 12, 42, 52, 84, 156, 186, 372, 1092, 1218, 1302, 1806, 2436, 2604, 2756, 3612, 4836, 5334, 7212, 8268, 10668, 12324, 15918, 18858, 24492, 31668, 31836, 33852, 37716, 37758, 46956, 50484, 52374, 55986, 57876, 71862, 75516, 86268

Offset: 1

Author

Alexander Adamchuk, Jan 05 2007

Keywords

• nonn

Comments

Subset of A067946 (numbers k such that k divides 5^k-1).

Links

• Robert Israel, Table of n, a(n) for n = 1..1000
• Taro Morishima, Über die Fermatsche Vermutung, Proc. Imp. Acad., Volume 4, Number 10 (1928), 590-592.

Crossrefs

Cf. A127100, A127101, A127102, A127103, A123104, A127106, A127107, A127092.

Cf. A067946 (numbers k such that k divides 5^k-1).

Programs

Maple

select(t -> (5 &^t - 1) mod (t^2) = 0, [$1..10^5]); # Robert Israel, Jul 15 2018

Mathematica

Select[Range[30000], IntegerQ[(PowerMod[5, #, #^2 ]-1)/#^2 ]&]

PARI

isok(n) = Mod(5, n^2)^n == 1; \\ Michel Marcus, Apr 23 2017

Extensions

More terms from Ryan Propper and Alexander Adamchuk, Jan 05 2007