On the Diophantine Equation $p^x + p^y = z^{2n}$
Dibyajyoti Deb
TL;DR
This paper generalizes and completely solves the Diophantine equation involving prime powers and perfect squares, extending previous work on specific cases for p=2 and 3.
Contribution
It provides a complete solution to the generalized equation $p^x + p^y = z^{2n}$, broadening the understanding of such exponential Diophantine equations.
Findings
Complete solutions for the generalized equation
Extension of previous results for p=2, 3
New insights into prime power equations
Abstract
In an earlier paper, Tatong and Suvarnamani explores the Diophantine equation for a prime number . In that paper they find some solutions to the equation for . In this paper, we look at a general version of this equation and solve it completely.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsChaos-based Image/Signal Encryption · Advanced Mathematical Theories and Applications · Algebraic Geometry and Number Theory