A328230 Numbers m that divide 3^(m + 1) + 1.

1, 2, 4, 5, 14, 244, 365, 434, 854, 2294, 3794, 5966, 7874, 10877, 26474, 33914, 117614, 188774, 231434, 284354, 487634, 501038, 589154, 593774, 621674, 755594, 1255814, 1306934, 1642094, 1911194, 2193124, 2434754, 2484674, 2507834, 2621654, 2643494, 3512114, 3759854, 3997574, 4082246

Offset: 1

Author

Juri-Stepan Gerasimov, Oct 08 2019

Keywords

• nonn

Comments

Conjecture: For k > 2, k^(m + 1) == -1 (mod m) has an infinite number of positive solutions.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1528 (n = 1..100 from Robert Israel)

Crossrefs

Cf. A055685, A277289, A296369.

Programs

Magma

[n+1: n in [0..5000000] | Modexp(3,n+2,n+1) eq n];

Maple

filter:= m -> 3 &^ (m+1) + 1 mod m = 0:
select(filter, [$1..10^7]); # Robert Israel, Oct 30 2019

PARI

isok(m) = Mod(3, m)^(m+1) == -1; \\ Michel Marcus, Oct 10 2019