The Diophantine Equation x^{2}+11^{m}=y^{n}
Gokhan Soydan, Musa Demirci, Ismail Naci Cangul
TL;DR
This paper provides a new proof for all solutions to the Diophantine equation x^2 + 11^m = y^n with specific conditions on m and n, advancing understanding of exponential Diophantine equations.
Contribution
It offers a novel proof for the solutions of x^2 + 11^m = y^n for odd m > 1 and n ≥ 3, extending previous results in number theory.
Findings
Complete characterization of solutions for the given equation.
New proof technique for exponential Diophantine equations.
Clarification of solution structure under specified conditions.
Abstract
The object of this paper is to give a new proof of all the solutions of the Diophantine equation x^2+11^m=y^n; in positive integers x, y with odd m>1 and n>=3.
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Mathematical Dynamics and Fractals