Siad Daboul - cp's OEIS frontend

User: Siad Daboul

Siad Daboul has authored 2 sequences.

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

Siad Daboul, Dec 27 2013

nonn

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

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.

Cf. A234535.

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

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

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

A234535 Numbers n such that n-1 is a divisor of 3^n + 5^n.

Original entry on oeis.org

2, 3, 5, 9, 18, 39, 153, 222, 378, 630, 1685, 1749, 3003, 8178, 10422, 41310, 70338, 103833, 141669, 151590, 285390, 385578, 542793, 578589, 804870, 816750, 950418, 1105893, 1132830, 1583778, 1585710, 1972809, 2578719, 2642430, 3248583, 3628089, 5875230, 6116253, 6152495, 6469470, 8550738, 9231834

Offset: 1

Siad Daboul, Dec 27 2013

nonn

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

Such n together with n^2 must belong to this sequence (an example is given by n=3). Furthermore, it is not known if the intersection of this sequence and A234536 equals {3}. - Max Alekseyev, May 19 2015

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

Cf. A234536.

Select[Range[2, 10^6], Mod[PowerMod[3, #, # - 1] + PowerMod[5, #, # - 1], # - 1] == 0 &]

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User: Siad Daboul

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

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