International Journal of Mathematics and Computer Science, Volume 20, Issue 4, Pages 1089-1095 , 01/01/2025
On the Exponential Diophantine Equation 9(5x) − py = z4
Abstract
In this article, we determine all solutions to the equation of the form 9(5<sup>x</sup>) − p<sup>y</sup> = z<sup>4</sup>, where p is a prime number and x,y,z are nonnegative integers. By employing elementary techniques involving congruences, we establish that the equation admits solutions only when both x and y are odd and p ≡ 29 or 149 (mod 240), or when (x,y,z,p) = (0,2,0,3) or (0,3,1,2).
Document Type
Article
Source Type
Journal
Keywords
Catalan’s ConjectureCongruences
ASJC Subject Area
Mathematics : Applied MathematicsMathematics : Computational MathematicsMathematics : Discrete Mathematics and CombinatoricsMathematics : Modeling and SimulationMathematics : Numerical AnalysisMathematics : Statistics and ProbabilityComputer Science : Computer Science (miscellaneous)Mathematics : Algebra and Number Theory