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A Variant of Fermat’s Diophantine Equation
Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Istanbul, Turkey
- 1 Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Istanbul, Turkey
Advances in Pure Mathematics·Volume 11 (2021)·Pages 929–936·Published 8 December 2021·DOI10.4236/apm.2021.1112059
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Abstract
A variant of Fermat’s last Diophantine equation is proposed by adjusting the number of terms in accord with the power of terms and a theorem describing the solubility conditions is stated. Numerically obtained primitive solutions are presented for several cases with number of terms equal to or greater than powers. Further, geometric representations of solutions for the second and third power equations are devised by recasting the general equation in a form with rational solutions less than unity. Finally, it is suggested to consider negative and complex integers in seeking solutions to Diophantine forms in general.
KeywordsVariant of Fermat’s Last EquationPositive Integer Solutions of New Fermat-Type EquationsGeometric Representations for Solutions of New Diophantine Equations
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