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A234536
Numbers k such that k+1 is a divisor of 3^k + 5^k.
3
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
1,2
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
Daniel Kohen et al., On Polynomials dividing Exponentials, MathOverflow.
MATHEMATICA
Select[Range[10^6], Mod[PowerMod[3, #, # + 1] + PowerMod[5, #, # + 1], # + 1] == 0 &]
PROG
(PARI) isok(k) = Mod(3, k+1)^k + Mod(5, k+1)^k == 0; \\ Michel Marcus, Aug 04 2021
CROSSREFS
Cf. A234535.
Sequence in context: A362651 A172995 A325476 * A103737 A354480 A108537
KEYWORD
nonn
AUTHOR
Siad Daboul, Dec 27 2013
EXTENSIONS
a(1) inserted by Amiram Eldar, Jul 31 2021
STATUS
approved