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Omni-MATH / Let n be an integer greater than or equal to 1. Find, as a function of n, the smallest integer k≥2 such that, among any k real numbers, there are necessarily two of which the diffe…

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problem

Let nn be an integer greater than or equal to 11. Find, as a function of nn, the smallest integer k≥2k\ge 2 such that, among any kk real numbers, there are necessarily two of which the difference, in absolute value, is either strictly less than 1/n1 / n, either strictly greater than nn.
Plain-text mathematical notation (without MathML)
Let n be an integer greater than or equal to 1. Find, as a function of n, the smallest integer k≥2 such that, among any k real numbers, there are necessarily two of which the difference, in absolute value, is either strictly less than 1/n, either  strictly greater than n.
Original LaTeX notation
Let $n$ be an integer greater than or equal to $1$. Find, as a function of $n$, the smallest integer $k\ge 2$ such that, among any $k$ real numbers, there are necessarily two of which the difference, in absolute value, is either strictly less than $1 / n$, either  strictly greater than $n$.

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Source and history

task_id
a106f31e-c48e-54ea-9d5c-462545a25693
task_key
test--a106f31e-c48e-54ea-9d5c-462545a25693
task_revision_id
1
config / split
/ test

Official source

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