Unsolvability of two diophantine equations of the form pᵃ + (p − 1)ᵇ = c²
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Date
April 24, 2024
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Publisher
International Journal of Mathematics and Computer Science
Abstract
In this research study, we use elementary methods in number theory to show that the Diophantine equations 11ᵃ + 10ᵇ = c² and 17ᵃ + 16ᵇ = c² are unsolvable in non-negative integers.
Description
Keywords
Diophantine equations, Number theory, Prime numbers, Exponential equations, Unsolvability, Algebraic structures, Algebraic structures
Citation
Gayo, W. S., & Siong, Venus D. (2024). Unsolvability of two diophantine equations of the form pᵃ + (p − 1)ᵇ = c². International Journal of Mathematics and Computer Science, 19(4), 1143-1145.