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- W2996609542 abstract "In this paper we introduce and develop the method of compression of points in space. We introduce the notion of the mass, the rank, the entropy, the cover and the energy of compression. We leverage this method to prove some class of inequalities related to Diophantine equations. In particular, we show that for each $L n-1$, there exist some $(x_1,x_2,ldots,x_n)in mathbb{N}^n$ with $x_ineq x_j$ for all $1leq i n-1$ there exist some $(x_1,x_2,ldots,x_n)$ with $x_ineq x_j$ for all $1leq i<jleq n$ and some $sgeq 2$ such that begin{align}sum limits_{j=1}^{n}frac{1}{x_j^s}gg sfrac{n}{L^{s-1}}.nonumber end{align}" @default.
- W2996609542 created "2019-12-26" @default.
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- W2996609542 date "2019-12-16" @default.
- W2996609542 modified "2023-09-27" @default.
- W2996609542 title "The Compression method and applications" @default.
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