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=7, b=-1, where U(m) is A054413(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)
LINKS
Dorin Andrica and Ovidiu Bagdasar, On Generalized Lucas Pseudoprimality of Level k, Mathematics (2021) Vol. 9, 838.
MATHEMATICA
Select[Range[3, 15000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 7]*Fibonacci[#, 7] - 1, #] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ovidiu Bagdasar, Oct 08 2020
STATUS
approved