Abstract
Objectives: This research article focuses on finding non-zero integer solutions to the Transcendental equation with six unknowns represented by . Methods: There is no universal method for finding integer solutions to Diophantine equations involving surds. Various substitutions strategies are employed to obtain non-zero distinct integer solutions to the surd equation under consideration. Findings: Five different choices of substitutions are utilized to determine many non-zero distinct integer solutions to the transcendental equation with six unknowns in title. Novelty: In this analysis, the transcendental equation with six unknowns given by has been reduced to either Space Pythagorean equation or non-homogeneous ternary quadratic equation through suitable transformations and for which integer solutions can be found elegantly. Keywords: Transcendental Equation With Six Unknowns, Surd Equation, Integer Solutions, Space Pythagorean Equation, Ternary Quadratic Equation
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