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Omni-MATH / Find all positive integers k<202 for which there exists a positive integer n such that {(n)/(202)}+{(2n)/(202)}+⋯+{(kn)/(202)}=(k)/(2) where {x} denote the fractional part of x.

Problem

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problem

Find all positive integers k<202k<202 for which there exists a positive integer nn such that {n202}+{2n202}+⋯+{kn202}=k2\left\{\frac{n}{202}\right\}+\left\{\frac{2 n}{202}\right\}+\cdots+\left\{\frac{k n}{202}\right\}=\frac{k}{2} where {x}\{x\} denote the fractional part of xx.
Plain-text mathematical notation (without MathML)
Find all positive integers k<202 for which there exists a positive integer n such that {(n)/(202)}+{(2n)/(202)}+⋯+{(kn)/(202)}=(k)/(2) where {x} denote the fractional part of x.
Original LaTeX notation
Find all positive integers $k<202$ for which there exists a positive integer $n$ such that $$\left\{\frac{n}{202}\right\}+\left\{\frac{2 n}{202}\right\}+\cdots+\left\{\frac{k n}{202}\right\}=\frac{k}{2}$$ where $\{x\}$ denote the fractional part of $x$.

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Source and history

task_id
c3a438ed-70af-59d7-ae83-db441e7555fd
task_key
test--c3a438ed-70af-59d7-ae83-db441e7555fd
task_revision_id
1
config / split
/ test

Official source

initial import