Authors:V. S. Akilandeswari
Abstract:In this paper, the all possible solutions of the Exponential Diophantine equation 3? + (3? + ?2) = ?2 with ? < ?, β as non-negative integers, also with the condition that β is not divisible by 3 and ?, ?, ? being non-negative integers, are found. The above Exponential Diophantine equation takes the solutions (?, ?, 1,0,2), (0,1,0,3,3), (1,0,0,1,2), (?, ?, ???3(1 + 2(3? + ?2)), 2,1 +(3? + ?2)), (?, ?, ???3 (3?(2? − 1 + 3?)), 1, ? + 3?), (?, ?, ???3(3?(3? − 2? − 1)), 1, 3?−?) for ? and β taking values in such a way that ???3(1 + 2(3? + ?2)), ???3(3?(2? − 1 + 3?)), ???3(3?(3? − 2? − 1)) takes only all possible integer values. Some of the examples are given for the possible values of ? and ?. It is easily witnessed here that, the solutions for the equation with larger values of ?, ? can be obtained by using these results.
Keywords: Exponential Diophantine Equation (EDE), Integer solutions.
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