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Omni-MATH / Find the minimum positive integer k such that there exists a function f from the set Bbb{Z} of all integers to {1,2,…k} with the property that f(x)≠f(y) whenever |x−y|∈{5,7,12}.

Problem

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problem

Find the minimum positive integer kk such that there exists a function ff from the set $\Bbb{Z}$ of all integers to {1,2,…k}\{1, 2, \ldots k\} with the property that f(x)≠f(y)f(x) \neq f(y) whenever |x−y|∈{5,7,12}|x-y| \in \{5, 7, 12\}.
Plain-text mathematical notation (without MathML)
Find the minimum positive integer k such that there exists a function f from the set $\Bbb{Z}$ of all integers to {1,2,…k} with the property that f(x)≠f(y) whenever |x−y|∈{5,7,12}.
Original LaTeX notation
Find the minimum positive integer $k$ such that there exists a function $f$ from the set $\Bbb{Z}$ of all integers to $\{1, 2, \ldots k\}$ with the property that $f(x) \neq f(y)$ whenever $|x-y| \in \{5, 7, 12\}$.

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Source and history

task_id
b69911b0-0bd3-5c7a-8cf8-82df2f99b2c6
task_key
test--b69911b0-0bd3-5c7a-8cf8-82df2f99b2c6
task_revision_id
1
config / split
/ test

Official source

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