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Omni-MATH / Let Z denote the set of all integers. Find all real numbers c>0 such that there exists a labeling of the lattice points (x,y)∈Z² with positive integers for which: only finitely man…

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problem

Let Z\mathbf{Z} denote the set of all integers. Find all real numbers c>0c > 0 such that there exists a labeling of the lattice points (x,y)∈Z2( x, y ) \in \mathbf{Z}^2 with positive integers for which: only finitely many distinct labels occur, and for each label ii , the distance between any two points labeled ii is at least cic^i .
Plain-text mathematical notation (without MathML)
Let Z denote the set of all integers. Find all real numbers c>0 such that there exists a labeling of the lattice points (x,y)∈Z² with positive integers for which: only finitely many distinct labels occur, and for each label i , the distance between any two points labeled i is at least c^(i) .
Original LaTeX notation
Let $\mathbf{Z}$ denote the set of all integers. Find all real numbers $c > 0$ such that there exists a labeling of the lattice points $( x, y ) \in \mathbf{Z}^2$ with positive integers for which: only finitely many distinct labels occur, and for each label $i$ , the distance between any two points labeled $i$ is at least $c^i$ .

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Source and history

task_id
aa8e50d2-7d13-5c6e-83a3-81d79df9c9a3
task_key
test--aa8e50d2-7d13-5c6e-83a3-81d79df9c9a3
task_revision_id
1
config / split
/ test

Official source

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