OFFSET
1,1
COMMENTS
The generalized Lucas sequence of integer parameters (a,b) is defined by
U(m+2) = a*U(m+1)-b*U(m) and U(0)=0, U(1)=1.
Whenever p is prime and b=-1,1 we have U^2(p) == 1 (mod p).
Here we define the odd composite integers for which U^2(m) == 1 (mod m) holds, for a=6, b=-1, where U(m) is A005668(m).
REFERENCES
D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer, 2020.
D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021)
MATHEMATICA
Select[Range[3, 15000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 6]*Fibonacci[#, 6] - 1, #] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ovidiu Bagdasar, Oct 08 2020
STATUS
approved