Unsolvability of two diophantine equations of the form pᵃ + (p − 1)ᵇ = c²

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creativework.keywordsDiophantine equation, integer solutions, Mihailescu’s Theorem, unsolvable.
dc.contributor.authorWilliam S. Gayo Jr.
dc.contributor.authorSiong, Venus D.
dc.date.accessioned2026-04-06T23:32:41Z
dc.date.available2026-04-06T23:32:41Z
dc.date.issuedApril 24, 2024
dc.description.abstractIn 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.
dc.identifier.citationGayo, 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.
dc.identifier.issne1814-0432
dc.identifier.urihttps://lakasa.dmmmsu.edu.ph/handle/123456789/1265
dc.language.isoen
dc.publisherInternational Journal of Mathematics and Computer Science
dc.relation.urihttps://future-in-tech.net/
dc.sdgSDG 4
dc.sdgSDG 4
dc.sdgSDG 9
dc.subjectDiophantine equations
dc.subjectNumber theory
dc.subjectPrime numbers
dc.subjectExponential equations
dc.subjectUnsolvability
dc.subjectAlgebraic structures
dc.subjectAlgebraic structures
dc.subject.ddcNumber theory
dc.subject.ddcDiophantine equations
dc.subject.lcshDiophantine equations
dc.subject.lcshNumber theory
dc.subject.lcshPrime numbers
dc.subject.lcshExponential equations
dc.subject.lcshMathematical proofs
dc.titleUnsolvability of two diophantine equations of the form pᵃ + (p − 1)ᵇ = c²
dc.typeArticle
oaire.citation.endPage1145
oaire.citation.issue4
oaire.citation.startPage1143
oaire.citation.volume19
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