Non-Negative Integer Solutions of Two Diophantine Equations 2<sup>x</sup> + 9<sup>y</sup> = z<sup>2</sup> and 5<sup>x</sup> + 9<sup>y</sup> = z<sup>2</sup>
Non-Negative Integer Solutions of Two Diophantine Equations 2<sup>x</sup> + 9<sup>y</sup> = z<sup>2</sup> and 5<sup>x</sup> + 9<sup>y</sup> = z<sup>2</sup>作者机构：Department of Mathematics Jahangirnagar University Dhaka Bangladesh
出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)
年 卷 期：2016年第4卷第4期
页 面：762-765页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Exponential Diophantine Equation Integer Solutions
摘 要：In this paper, we study two Diophantine equations of the type px + 9y = z2 , where p is a prime number. We find that the equation 2x + 9y = z2 has exactly two solutions (x, y, z) in non-negative integer i.e., {(3, 0, 3),(4, 1, 5)} but 5x + 9y = z2 has no non-negative integer solution.
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