SOLUTION OF THE EXPONENTIAL DIOPHANTINE EQUATION.

Pailin  Chayapham; Komon  Paisal; Wichan  Lertlop; Pachoke  Lert-asavapatra

Pailin Chayapham Faculty of Science and Technology, ****College of innovation and management, Suan Sunandha Rajabhat University, Bangkok, Thailand
Komon Paisal Faculty of Science and Technology, Suan Sunandha Rajabhat University, Bangkok, Thailand
Wichan Lertlop Faculty of Science and Technology, Suan Sunandha Rajabhat University, Bangkok, Thailand
Pachoke Lert-asavapatra Faculty of Science and Technology, Suan Sunandha Rajabhat University, Bangkok, Thailand

Keywords: Diophantine equation, integer solution, odd prime

Abstract

In this research, we consider the Diophantine equation 8x 131y  z2 where x, y and z
were non-negative integers. This study aims at obtaining the solution of this equation.
Catalan’s conjecture is used to solve the solution. To propose Catalan’s conjecture for the Diophantine equation 1 x y a b  that has a unique solution. We have exactly solution  x, y, z  in non-negative integers and find that it has a unique solution, that is  x, y, z   1,0,3 Then, we prove that (1,0,3) is a unique non-negative integer solution of this Diophantine equation.