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Generalized Fibonacci and Lucas sequences (Un) and (Vn) are defined by the recurrence relations Un+1 = PUn+QUn−1 and Vn+1 = PVn +QVn−1, n ≥ 1, with initial conditions U0 = 0, U1 = 1 and V0 = 2, V1 = P. This paper deals with Fibonacci and Lucas numbers of the form Un(P,Q) and Vn(P,Q) with the special consideration that P ≥ 3 is odd and Q = −1. Under these consideration, we solve the equations Vn = 5kx2, Vn = 7kx2, Vn = 5kx2±1, and Vn = 7kx2±1 when k | P with k > 1. Moreover, we solve the equations Vn = 5x2 ±1 and Vn = 7x2 ± 1.
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참고문헌 (14)
참고문헌 신청
B. Demirt¨urk / 2009 / Integer solutions of some Diophantine equations via Fi-bonacci and Lucas numbers / J. Integer Seq 12 (8) : 14 ~
D. Kalman / 2003 / The Fibonacci numbers-exposed / Math. Mag 76 (3) : 167 ~ 181
J. B. Muskat / 1993 / Generalized Fibonacci and Lucas sequences and rootfinding methods / Math. Comp 61 (203) : 365 ~ 372
J. H. E. Cohn / 1972 / Squares in some recurrent sequences / Pacific J. Math 41 : 631 ~ 646
P. Ribenboim / 1996 / The square terms in Lucas sequences / J. Number Theory 58 (1) : 104 ~ 123
D. Kalman / 2003 / The Fibonacci numbers-exposed / Math. Mag 76 (3) : 167 ~ 181
J. B. Muskat / 1993 / Generalized Fibonacci and Lucas sequences and rootfinding methods / Math. Comp 61 (203) : 365 ~ 372
J. H. E. Cohn / 1972 / Squares in some recurrent sequences / Pacific J. Math 41 : 631 ~ 646
P. Ribenboim / 1996 / The square terms in Lucas sequences / J. Number Theory 58 (1) : 104 ~ 123
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