Representation of $\frac{1}{2}(L_n-1)(L_{n+1}-1)$ and $\frac{1}{2}(L_n-1)(L_{n+2}-1)$
Abstract
Let Ln be the Lucas sequence: L1 = 1, L2 = 3, and Ln = Ln-1 + Ln-2 for n ∈ Z.We obtain new identities involving Lucas numbers from the Diophantine equations ax + by = (a -1)(b -1)/2 and ax + by + 1 = (a -1)(b -1)/2 when (a, b) = (Ln, Ln+1) and (Ln, Ln+2) for n ≥ 0.
Fields of Study & Subjects
Finite Group Theory Research
Algebraic structures and combinatorial models
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Asia Pacific Journal of Mathematics
- Volume
- 13
- Pages
- 3–3
- Publication date
- 1 January 2026