|
Brahmagupta Triangles in Generalized Fibonacci Sequences |
|---|---|
| รหัสดีโอไอ | |
| Creator | Sompong Chuysurichay |
| Title | Brahmagupta Triangles in Generalized Fibonacci Sequences |
| Contributor | Kanwara Mukkhata |
| Publisher | Faculty of Science, Khon Kaen University |
| Publication Year | 2569 |
| Journal Title | KKU Science Journal |
| Journal Vol. | 54 |
| Journal No. | 2 |
| Page no. | 530-537 |
| Keyword | Brahmagupta Triangle, Heron Triangle, Generalized Fibonacci Sequence |
| URL Website | https://ph01.tci-thaijo.org/index.php/KKUSciJ |
| Website title | Thai Journal Online (ThaiJO) |
| ISSN | 3027-6667 |
| Abstract | For any positive integers α and β, define the sequence (G_n (α,β)) by G_1=α, G_2=β, and G_n=G_(n-1)+G_(n-2) for all n≥3. A Brahmagupta triangle is a triangle all of whose side lengths are consecutive positive integers with integral area. In this paper, we prove that for any given α and β, there is at most one Brahmagupta triangle all of whose side lengths are elements of (G_n (α,β)). Moreover, we characterize all initial values (α,β) for which the sequence (G_n (α,β)) contains a Brahmagupta triangle, and show that this occurs precisely in two Pell-parametrized families. |
