Nobuhisa Abe
Abstract
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Let $\mathbf{N}$ denote the set of natural numbers $\{1, 2, 3, \ldots\}$. $n$ being an odd natural number, we consider the Diophantine equation as mentioned in the title and solve it completely for $n \leq 15$, i.e. find all $(x,y) \in \mathbf{N}^2$ satisfying this equation.
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Let $\mathbf{N}$ denote the set of natural numbers $\{1, 2, 3, \ldots\}$. $n$ being an odd natural number, we consider the Diophantine equation as mentioned in the title and solve it completely for $n \leq 15$, i.e. find all $(x,y) \in \mathbf{N}^2$ satisfying this equation.
Key concepts: Diophantine equation, Natural number, Mathematics, Combinatorics, Discrete mathematics