A p-adic look at the Diophantine equation x^{2}+11^{2k}=y^{n}

TL;DR

This paper completely solves the Diophantine equation x^2 + 11^{2k} = y^n for positive integers, providing a p-adic perspective and identifying all solutions.

Contribution

It offers a complete solution to the equation with a novel p-adic interpretation, extending understanding of such exponential Diophantine equations.

Findings

All solutions for x, y, n, k are explicitly determined.

A p-adic framework is used to analyze the equation.

The results contribute to the theory of exponential Diophantine equations.

Abstract

We find all solutions of Diophantine equation x^{2}+11^{2k} = y^{n} where x>=1, y>=1, n>=3 and k is natural number. We give p-adic interpretation of this equation.