We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
PERFECT POWERS THAT ARE SUMS OF TWO POWERS OF FIBONACCI NUMBERS.
- Authors
ZHANG, ZHONGFENG; TOGBÉ, ALAIN
- Abstract
In this paper, we consider the Diophantine equations $$\begin{eqnarray}\displaystyle F_{n}^{q}\pm F_{m}^{q}=y^{p} & & \displaystyle \nonumber\end{eqnarray}$$ with positive integers $q,p\geq 2$ and $\gcd (F_{n},F_{m})=1$ , where $F_{k}$ is a Fibonacci number. We obtain results for $q=2$ or $q$ an odd prime with $q\equiv 3\;(\text{mod}\;4),3 , and complete solutions for $q=3$.
- Subjects
DIOPHANTINE equations; INTEGERS; FIBONACCI sequence; EXPONENTIAL functions; MATHEMATICS theorems
- Publication
Bulletin of the Australian Mathematical Society, 2019, Vol 99, Issue 1, p34
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972718000916