References

POWERS IN THE LUCAS SEQUENCE WHEN THE INDEX IS DIVISIBLE BY THREE


[1] M. A. Bennett, Powers in recurrence sequences: Pell equations, Transactions of the American Mathematical Society 357 (2004), 1675-1691.

[2] A. Bremner and N. Tzanakis, Lucas sequences whose 12th or 9th term is a square, J. Number Theory 107 (2004), 215-227.

[3] Y. Bugeaud, M. Mignotte and S. Siksek, Classical and modular approaches to exponential Diophantine equations, I, Fibonacci and Lucas perfect powers, Annals of Math. 163 (2006), 969-1018.

[4] J. H. E. Cohn, Perfect Pell powers, Glasgow Mathematical Journal 38(1) (1996), 19-20.

[5] H. Darmon and L. Merel, Winding quotients and some variants of Fermat’s last theorem, J. Reine Angew. Math. 490 (1997), 81-100.

[6] T. Kagawa and N. Terai, Squares in Lucas sequences and some Diophantine equations, Manuscripta Math. 96 (1998), 195-202.

[7] M. Le, On the Diophantine equation Acta Arithmetica 82(1) (1997), 17-26.

[8] P. Mihailescu, Primary ciclotomic units and a proof of Catalan’s conjecture, J. Reine Angew. Math. 572 (2004), 167-195.

[9] P. Ribenboim and W. L. McDaniel, The square terms in Lucas sequences, J. Number Theory 58 (1996), 104-122.