TITLE:
A Variant of Fermat’s Diophantine Equation
AUTHORS:
Serdar Beji
KEYWORDS:
Variant of Fermat’s Last Equation, Positive Integer Solutions of New Fermat-Type Equations, Geometric Representations for Solutions of New Diophantine Equations
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.11 No.12,
December
8,
2021
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.