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Omni-MATH / Does there exists a positive irrational number x, such that there are at most finite positive integers n, satisfy that for any integer 1≤k≤n, {kx}geqfrac 1{n+1}?

Problem

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problem

Does there exists a positive irrational number x,{x}, such that there are at most finite positive integers n,{n}, satisfy that for any integer 1≤k≤n,1\leq k\leq n, $\{kx\}\geq\frac 1{n+1}?$
Plain-text mathematical notation (without MathML)
Does there exists a positive irrational number x, such that there are at most finite positive integers n, satisfy that for any integer 1≤k≤n, $\{kx\}\geq\frac 1{n+1}?$
Original LaTeX notation
Does there exists a positive irrational number ${x},$ such that there are at most finite positive integers ${n},$ satisfy that for any integer $1\leq k\leq n,$ $\{kx\}\geq\frac 1{n+1}?$

Discussion

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Source and history

task_id
b4c944c0-c5b2-500f-9da7-0592ad6b0f01
task_key
test--b4c944c0-c5b2-500f-9da7-0592ad6b0f01
task_revision_id
1
config / split
/ test

Official source

initial import