A234536 Numbers k such that k+1 is a divisor of 3^k + 5^k.

1, 3, 7, 75, 2355, 11475, 31995, 57075, 80311, 196185, 215325, 335115, 991875, 1009545, 1038375, 1169715, 1185675, 1193655, 3507751, 5503095, 8412525, 8618475, 8670915, 9513075, 11384343, 12689415, 13587735, 13708695, 14101815, 14841255, 16002525, 17409015, 21856635, 22195875, 22307805, 25948755

Offset: 1

Author

Siad Daboul, Dec 27 2013

Keywords

• nonn

Comments

It is an open problem to find all numbers k such that (k+1)*(k-1) is a divisor of 3^k + 5^k.

In particular, it is not known if the intersection of this sequence and A234535 equals {3}. - Max Alekseyev, May 19 2015

Links

• Amiram Eldar, Table of n, a(n) for n = 1..600
• Daniel Kohen et al., On Polynomials dividing Exponentials, MathOverflow.
• Byron Schmuland et al., Find all positive integers n such that 3^n + 5^n is divisible by n^2 - 1, Math StackExchange.

Crossrefs

Cf. A234535.

Programs

Mathematica

Select[Range[10^6], Mod[PowerMod[3, #, # + 1] + PowerMod[5, #, # + 1], # + 1] == 0 &]

PARI

isok(k) = Mod(3, k+1)^k + Mod(5, k+1)^k == 0; \\ Michel Marcus, Aug 04 2021

Extensions

a(1) inserted by Amiram Eldar, Jul 31 2021