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

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

Author

Siad Daboul, Dec 27 2013

Keywords

• nonn

Comments

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

Links

• 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. A234536.

Programs

Mathematica

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