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• 1 Department of Mathematics and Statistics, University of Calgary & Department of Geometry Eötvös Loránd University 2500 University Drive N.W., Calgary, AB, T2N 1N4, Canada & Pázmány Péter sétány 1/c H-1117 Budapest, Hungary 2500 University Drive N.W., Calgary, AB, T2N 1N4, Canada & Pázmány Péter sétány 1/c H-1117 Budapest, Hungary
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## Summary

The Illumination Conjecture was raised independently by Boltyanski and Hadwiger in 1960. According to this conjecture any \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $d$ \end{document}-dimensional convex body can be illuminated by at most \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $2^d$ \end{document} light sources. This is an important fundamental problem. The paper surveys the state of the art of the Illumination Conjecture.

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