PERFECT POWERS THAT ARE SUMS OF TWO POWERS OF FIBONACCI NUMBERS
2018 ◽
Vol 99
(1)
◽
pp. 34-41
Keyword(s):
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 $q\equiv 3\;(\text{mod}\;4),3<q<1087$, and complete solutions for $q=3$.
2020 ◽
Vol 16
(09)
◽
pp. 2095-2111
Keyword(s):
2019 ◽
Vol 15
(05)
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pp. 1069-1074
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1961 ◽
Vol 5
(1)
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pp. 35-40
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1990 ◽
Vol 34
(2)
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pp. 235-250
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1991 ◽
Vol 43
(3)
◽
pp. 387-392
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1966 ◽
Vol 62
(4)
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pp. 637-642
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Keyword(s):