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On Integer Solutions to Exponential Diophantine Equations Arising from Centered Tetradecagonal and Pronic Bases
Abstract
This study investigates two forms of exponential Diophantine equations that are built upon special numerical structures: centered tetradecagonal numbers and pronic numbers. The primary focus lies in determining the existence of integer solutions for each equation. It is shown that for one of the equations, there exists a unique solution in the set of whole numbers for all values of the parameter greater than one. In contrast, the second equation exhibits a consistent pattern of solutions across all positive integers. Additionally, several particular instances are examined to further support and illustrate the general results.
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