Maciej Zakarczemny

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20242026

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math.NT2026

On the Diophantine Equation Involving Elementary Symmetric Polynomials and the Decomposition of Unity

Sándor Z. Kiss, Csaba Sándor, Maciej Zakarczemny

We consider the equality of the values of the $n$ th and $k$ th elementary symmetric polynomials of $n$ not necessarily distinct positive integers. For $k < n$ , we prove that this eq…

math.NT2024

Equal Sum and Product Problem III

Csaba Sándor, Maciej Zakarczemny

Denote by $N (n)$ the number of integer solutions $(x_{1}, x_{2}, \dots, x_{n})$ of the equation $x_{1} + x_{2} + \dots + x_{n} = x_{1} x_{2} \cdot \dots \cdot x_{n}$ such that $x_1\ge x_2\ge\ldots\ge x_n\ge…