William S. Gayo Jr.Siong, Venus D.2026-04-062026-04-06April 24,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.e1814-0432https://lakasa.dmmmsu.edu.ph/handle/123456789/1265In 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.enDiophantine equationsNumber theoryPrime numbersExponential equationsUnsolvabilityAlgebraic structuresAlgebraic structuresNumber theoryDiophantine equationsDiophantine equationsNumber theoryPrime numbersExponential equationsMathematical proofsArticle