On the Diophantine Equation n^x + 10^y = z^2

Q3 Mathematics

WSEAS Transactions on Mathematics Pub Date : 2023-02-23 DOI:10.37394/23206.2023.22.19

S. Tadee

引用次数: 1

Abstract

In this paper, we show that (n, x, y, z) = (2, 3, 0, 3) is the unique non-negative integer solution of the Diophantine equation n^x + 10^y = z^2 , where n is a positive integer with n ≡ 2 (mod 30) and x, y, z are non-negative integers. If n = 5, then the Diophantine equation has exactly one non-negative integer solution (x, y, z) = (3, 2, 15). We also give some conditions for non-existence of solutions of the Diophantine equation.

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丢番图方程n^x + 10^y = z^2

本文证明(n, x, y, z) =(2,3,0,3)是丢芬图方程n^x + 10^y = z^2的唯一非负整数解，其中n为n≡2 (mod 30)的正整数，x, y, z为非负整数。如果n = 5，则丢芬图方程只有一个非负整数解(x, y, z) =(3,2,15)。给出了丢番图方程解不存在的一些条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.