A234535 - OEIS

%I #21 Jun 19 2015 06:40:35

%S 2,3,5,9,18,39,153,222,378,630,1685,1749,3003,8178,10422,41310,70338,

%T 103833,141669,151590,285390,385578,542793,578589,804870,816750,

%U 950418,1105893,1132830,1583778,1585710,1972809,2578719,2642430,3248583,3628089,5875230,6116253,6152495,6469470,8550738,9231834

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

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

%C 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

%H Daniel Kohen et al., <a href="http://mathoverflow.net/questions/16341/on-polynomials-dividing-exponentials">On Polynomials dividing Exponentials</a>, MathOverflow

%H Byron Schmuland et al., <a href="http://math.stackexchange.com/questions/612346/">Find all positive integers n such that 3^n + 5^n is divisible by n^2 - 1</a>, Math StackExchange

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

%Y Cf. A234536.

%K nonn

%O 1,1

%A _Siad Daboul_, Dec 27 2013