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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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Let P ≥ 3 be an integer and let (Un) and (Vn) denote gen- eralized Fibonacci and Lucas sequences defined by U0 = 0, U1 = 1; V0 = 2, V1 = P, and Un+1 = PUn − Un−1, Vn+1 = PVn − Vn−1 for n ≥ 1. In this study, when P is odd, we solve the equations Vn = kx2 and Vn = 2kx2 with k | P and k > 1. Then, when k | P and k > 1, we solve some other equations such as Un = kx2,Un = 2kx2,Un = 3kx2, Vn = kx2 ∓ 1, Vn = 2kx2 ∓1, and Un = kx2 ∓1. Moreover, when P is odd, we solve the equations Vn = wx2 +1 and Vn = wx2 −1 for w = 2, 3, 6. After that, we solve some Diophantine equations.
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참고문헌 (17)
참고문헌 신청
D. Kalman / 2003 / The Fibonacci numbersexposed / 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
J. P. Jones / 2003 / Representation of solutions of Pell equations using Lucas sequences / Acta Academia Pead. Agr., Sectio Mathematicae 30 : 75 ~ 86
P. Ribenboim / 1996 / The square terms in Lucas sequences / J. Number Theory 58 (1) : 104 ~ 123
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
J. P. Jones / 2003 / Representation of solutions of Pell equations using Lucas sequences / Acta Academia Pead. Agr., Sectio Mathematicae 30 : 75 ~ 86
P. Ribenboim / 1996 / The square terms in Lucas sequences / J. Number Theory 58 (1) : 104 ~ 123
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