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- Title
REPDIGITS AS DIFFERENCE OF TWO FIBONACCI OR LUCAS NUMBERS.
- Authors
BHOI, K.; RAY, P. K.
- Abstract
In the present study we investigate all repdigits which are expressed as a difference of two Fibonacci or Lucas numbers. We show that if Fn-Fm is a repdigit, where Fn denotes the n-th Fibonacci number, then (n,m) ∈ {(7, 3), (9, 1), (9, 2), (11, 1), (11, 2), (11, 9), (12, 11), (15, 10)}. Further, if Ln denotes the n-th Lucas number, then Ln - Lm is a repdigit for (n,m) ∈ {(6, 4), (7, 4), (7, 6), (8, 2)}, where n > m. Namely, the only repdigits that can be expressed as difference of two Fibonacci numbers are 11, 33, 55, 88 and 555; their representations are 11 = F7 - F3, 33 = F9 - F1 = F9 - F2, 55 = F11 - F9 = F12 - F11, 88 = F11 - F1 = F11 - F2, 555 = F15 - F10 (Theorem 2). Similar result for difference of two Lucas numbers: The only repdigits that can be expressed as difference of two Lucas numbers are 11, 22 and 44; their representations are 11 = L6 - L4 = L7 - L6, 22 = L7 - L4, 4 = L8 - L2 (Theorem 3).
- Subjects
LUCAS numbers; FIBONACCI sequence; DIOPHANTINE equations; NUMBER theory; POLYNOMIALS
- Publication
Matematychni Studii, 2021, Vol 56, Issue 2, p124
- ISSN
1027-4634
- Publication type
Article
- DOI
10.30970/ms.56.2.124-132