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arXiv · 2001.07936

Determination of the asymptotic behavior of the number of natural solutions for certain types of diagonal Diophantine equations

Victor Volfson
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Abstract

We obtain asymptotic upper bounds for the number of natural solutions of the following diagonal Diophantine equations in a hypercube with side - $N$ in the paper: $x_1 = x_2^k+...+x_s^k$, $x_1^k = x_2^k+...+x_s^k$, $x_1 = \sum_{j=2}^s {x_j}^{k_j}$, where $k,s,k_j$ are the natural numbers.

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Victor Volfson. 2020-01-22. Determination of the asymptotic behavior of the number of natural solutions for certain types of diagonal Diophantine equations. https://arxiv.org/abs/2001.07936

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