The View-Obstruction Problem forn-Dimensional Cubes

Yong Gao Chen; T. W. Cusick

doi:10.1006/jnth.1998.2309

The View-Obstruction Problem forn-Dimensional Cubes

Yong Gao Chen
, T. W. Cusick

Mathematics

Nanjing Normal University

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

The view-obstruction problem for then-dimensional cube is equivalent to the conjecture that for anynpositive integersv₁,...,v_nthere is a real numberxsuch that each v_ix≥(n+1)^-1(here y denotes the distance fromyto the nearest integer). This conjecture has been previously solved forn≤4. In this paper we prove that when 2n-3 is a prime andn≥4 we can find a real numberxwhich gives each v_ix≥1/(2n-3). In fact more than this is proved.

Original language	English
Pages (from-to)	126-133
Number of pages	8
Journal	Journal of Number Theory
Volume	74
Issue number	1
DOIs	https://doi.org/10.1006/jnth.1998.2309
State	Published - Jan 1999

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abstract = "The view-obstruction problem for then-dimensional cube is equivalent to the conjecture that for anynpositive integersv1,...,vnthere is a real numberxsuch that each vix≥(n+1)-1(here y denotes the distance fromyto the nearest integer). This conjecture has been previously solved forn≤4. In this paper we prove that when 2n-3 is a prime andn≥4 we can find a real numberxwhich gives each vix≥1/(2n-3). In fact more than this is proved.",

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The View-Obstruction Problem forn-Dimensional Cubes

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