(International Journal of Mathematics and Computer Science, April 24, 2024) William S. Gayo Jr.; Siong, Venus D.
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.