A note on consecutive integers of the form 2<sup><em>x</em></sup> + <em>y</em><sup><em>2</em></sup>

A note on consecutive integers of the form 2<sup><em>x</em></sup> + <em>y</em><sup><em>2</em></sup>

Let $k$ be a positive integer with $k\ge 2$. Let $N_k$ denote the number of $k$ tuples of consecutive integers with each of them in the form $2^x+y^2$, where $x,y$ are nonnegative integers. In this paper, we investigate the formulas for $N_k$. Actually, by using some elementary methods, we show that...

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Bibliographic Details
Main Authors: Zongbing Lin, Kaimin Cheng
Format: Article
Language:English
Published: AIMS Press 2020-06-01
Series:AIMS Mathematics
Subjects:
diophantine equation
consecutive integers
sum of two powers
Online Access:https://www.aimspress.com/article/10.3934/math.2020285/fulltext.html

Internet

https://www.aimspress.com/article/10.3934/math.2020285/fulltext.html

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