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We explicitly solve the diophantine equations of the form $$ A_{n_1}A_{n_2}\cdots A_{n_k}\pm 1 = B_m^2, $$ where $(A_n)_{n\geq 0}$ and $(B_m)_{m\geq 0}$ are either the Fibonacci sequence or Lucas sequence. This extends the result of D. Marques \cite{Mar} and L. Szalay \cite{Sza} concerning a variant of Brocard-Ramanujan equation.
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참고문헌 (14)
참고문헌 신청
B. C. Berndt / 2006 / On the Brocard–Ramanujan Diophantine equation n! + 1 = m2 / Ramanujan J 4(1):41~42
Y. Bilu / 2001 / Existence of primitive divisors of Lucas and Lehmer numbers / J. Reine Angew. Math 539:75~122
Brother A. Brousseau / 1972 / Fibonacci and Related Number Theoretic Tables / The Fibonacci Association
R. D. Carmichael / 1913 / On the numerical factors of the arithmetic forms αn ± βn / Ann. of Math.(2) 15:30~48
A. D¸abrowski / 2012 / On the Brocard–Ramanujan problem and generalizations / Colloq. Math 126(1):105~110
Y. Bilu / 2001 / Existence of primitive divisors of Lucas and Lehmer numbers / J. Reine Angew. Math 539:75~122
Brother A. Brousseau / 1972 / Fibonacci and Related Number Theoretic Tables / The Fibonacci Association
R. D. Carmichael / 1913 / On the numerical factors of the arithmetic forms αn ± βn / Ann. of Math.(2) 15:30~48
A. D¸abrowski / 2012 / On the Brocard–Ramanujan problem and generalizations / Colloq. Math 126(1):105~110
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