On the exponential Diophantine equation \(p^x+q^y=z^3\): theorems and conjectures.(English)Zbl 1496.11057
Giri, Debasis (ed.) et al., Proceedings of the seventh international conference on mathematics and computing, ICMC 2021, Shibpur, India, March 2–5, 2021. Singapore: Springer. Adv. Intell. Syst. Comput. 1412, 711-723 (2022).
Summary: In this work, we solve the Diophantine equations \(p^x+q^y=z^3\) in the set of nonnegative integers. We consider twin primes \(p \text{ and} q\) having the following forms:
For the entire collection see [Zbl 1491.65006].
- (a)
- twin primes of the form \(8N+1\) and \(8N+3\) for some \(N\in \mathbb{N}_0\),
- (b)
- twin primes of the form \(8N+3\) and \(8N+5\) for some \(N\in \mathbb{N}_0\),
- (c)
- twin primes of the form \(8N+5\) and \(8N+7\) for some \(N\in \mathbb{N}_0\), and
- (d)
- twin primes of the form \(8N+7\) and \(8N+9\) for some \(N\in \mathbb{N}_0\).
For the entire collection see [Zbl 1491.65006].
MSC:
| 11D61 | Exponential Diophantine equations |
Cite
Full Text:DOI
References:
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