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Omni-MATH / Given a positive integer k, let …k and the nearest perfect square. For example, …n such that (‖1‖+‖2‖+⋯+‖n‖)/(n)=100.

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problem

Given a positive integer kk, let \|k\| denote the absolute difference between kk and the nearest perfect square. For example, \|13\|=3 since the nearest perfect square to 13 is 16. Compute the smallest positive integer nn such that ‖1‖+‖2‖+⋯+‖n‖n=100\frac{\|1\|+\|2\|+\cdots+\|n\|}{n}=100.
Plain-text mathematical notation (without MathML)
Given a positive integer k, let \|k\| denote the absolute difference between k and the nearest perfect square. For example, \|13\|=3 since the nearest perfect square to 13 is 16. Compute the smallest positive integer n such that (‖1‖+‖2‖+⋯+‖n‖)/(n)=100.
Original LaTeX notation
Given a positive integer $k$, let \|k\| denote the absolute difference between $k$ and the nearest perfect square. For example, \|13\|=3 since the nearest perfect square to 13 is 16. Compute the smallest positive integer $n$ such that $\frac{\|1\|+\|2\|+\cdots+\|n\|}{n}=100$.

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Source and history

task_id
e59f0e6b-fd15-59e0-9d2b-09666d4740d4
task_key
test--e59f0e6b-fd15-59e0-9d2b-09666d4740d4
task_revision_id
1
config / split
/ test

Official source

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