On the number of integers which form perfect powers in the way of $ x(y_1^2+y_2^2+y_3^2+y_4^2) = z^k $

On the number of integers which form perfect powers in the way of $ x(y_1^2+y_2^2+y_3^2+y_4^2) = z^k $

<p>Let $ k \geqslant 2 $ be an integer. We studied the number of integers which form perfect $ k $-th powers in the way of</p> <p class="disp_formula">$ x(y_1^2+y_2^2+y_3^2+y_4^2) = z^k. $</p> <p>For $ k \geqslant4 $, we established a unified asymptoti...

Full description

Bibliographic Details
Main Author: Tingting Wen
Format: Article
Language:English
Published: AIMS Press 2024-02-01
Series:AIMS Mathematics
Subjects:
counting solutions of diophantine equations
perfect powers
double dirichlet series
Online Access:https://www.aimspress.com/article/doi/10.3934/math.2024423?viewType=HTML

Internet

https://www.aimspress.com/article/doi/10.3934/math.2024423?viewType=HTML

Similar Items