논문KCI 등재
On the Diophantine equation $a \left(\frac{b^k - 1}{b - 1}\right) = U_n – U_m$
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초록
Let $b$ be an integer such that $ b \geqslant2$. In this paper, we show that there are only finitely many repdigits in base $b$ which can be written as difference of two generalized Lucas numbers. In addition, we completely solve the considered Diophantine equation with the Pell sequence using the decimal base.
Abstract
Let $b$ be an integer such that $ b \geqslant2$. In this paper, we show that there are only finitely many repdigits in base $b$ which can be written as difference of two generalized Lucas numbers. In addition, we completely solve the considered Diophantine equation with the Pell sequence using the decimal base.
참고문헌 (15)
- M. G. Duman, "Padovan numbers as difference of two repdigits, Indian", Journal of Pure and Applied Mathematics (2023)[DOI]
- B. Faye, "Pell and Pell-Lucas numbers with only one distinct digit", Ann. Math. Inform, 45, pp.55~60 (2015)
- R. Keskin, "Repdigits as the difference of two Pell or Pell-Lucas numbers", Korean J. Math, 31(1), pp.63~73 (2023)
- B. Edjeou, "Pell and Pell-Lucas numbers as the difference of two repdigits", Afr. Mat, 34(4) (2023)
- Z. Siar, "Repdigits base b as the difference of two Fibonacci numbers", J. Math. Study, 55(1), pp.84~94 (2022)
- F. Luca, "Fibonacci and Lucas numbers with only one distinct digit", Port. Math, 57(02), pp.243~254 (2000)
- F. Erduvan, "Fibonacci and Lucas numbers as the difference of two repdigits", Rend. Circ. Mat. Palermo II, 71, pp.575~589 (2021)
- P. Ray, "Repdigits as difference of two Fibonacci or Lucas numbers", Mat. Stud, 56, pp.124~132 (2021)
- P. Ribenboim, "My Numbers, My Friends: Popular Lectures on Number Theory" (2000), Springer
- K. N. Ad´edji, "Padovan and Perrin Numbers as Products of Two Generalized Lucas Numbers", Arch. Math. (Brno), 59, pp.351~373 (2023)
- E. M. Matveev, "An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers II", Izv. Math, 64(6), pp.1217~1269 (2000)
- A. Baker, "The equations 3x2 − 2 = y2 and 8x2 − 7 = z2", Quart.J of Math. Ser, 20(2), pp.129~137 (1969)
- A. Dujella, "A generalization of a theorem of Baker and Davenport", Quart. J. Math. Oxford Ser, 49(3), pp.291~306 (1998)
- J.J. Bravo, "Powers of two as sums of two k-Fibonacci numbers", Miskolc Math. Notes, 17(1), pp.85~100 (2016)
- S. G. Sanchez, "Linear combinations of factorials and S-units in a binary recurrence sequence", Ann. Math. Qu´e, 38, pp.169~188 (2014)
관련 논문AI추천
Repdigits as difference of two Pell or Pell-Lucas numbersFatih Erduvan, Refik Keskin강원경기수학회 · 한국수학논문집2023 · 제31권 제1호Fibonacci and Lucas Numbers Associated with Brocard-Ramanujan EquationPrapanpong Pongsriiam대한수학회 · 대한수학회논문집2017 · 제32권 제3호GENERALIZED FIBONACCI AND LUCAS NUMBERS OF THE FORM wx 2 AND wx 2 ∓ 1Refik Keskin대한수학회 · 대한수학회보2014 · 제51권 제4호On the intersection of $k$-Fibonacci and Pell numbersCarlos A. Gomez, Jhon J. Bravo, Jose L. Herrera대한수학회 · 대한수학회보2019 · 제56권 제2호GENERALIZED LUCAS NUMBERS OF THE FORM 5kx2 AND 7kx2Olcay Karaatli, Refik Keskin대한수학회 · 대한수학회보2015 · 제52권 제5호The extendibility of Diophantine pairs with property $D(-1)$박진서강원경기수학회 · 한국수학논문집2020 · 제28권 제3호
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