TITLE:
Non-Negative Integer Solutions of Two Diophantine Equations 2x + 9y = z2 and 5x + 9y = z2
AUTHORS:
Md. Al-Amin Khan, Abdur Rashid, Md. Sharif Uddin
KEYWORDS:
Exponential Diophantine Equation, Integer Solutions
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.4,
April
27,
2016
ABSTRACT: 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.