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Omni-MATH / Let ⌊x⌋ denote the largest integer less than or equal to x, and let {x} denote the fractional part of x. For example, ⌊π⌋=3, and {π}=0.14159…, while ⌊100⌋=100 and {100}=0. If n is …

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problem

Let ⌊x⌋\lfloor x\rfloor denote the largest integer less than or equal to xx, and let {x}\{x\} denote the fractional part of xx. For example, ⌊π⌋=3\lfloor\pi\rfloor=3, and {π}=0.14159…\{\pi\}=0.14159 \ldots, while ⌊100⌋=100\lfloor 100\rfloor=100 and {100}=0\{100\}=0. If nn is the largest solution to the equation ⌊n⌋n=20152016\frac{\lfloor n\rfloor}{n}=\frac{2015}{2016}, compute {n}\{n\}.
Plain-text mathematical notation (without MathML)
Let ⌊x⌋ denote the largest integer less than or equal to x, and let {x} denote the fractional part of x. For example, ⌊π⌋=3, and {π}=0.14159…, while ⌊100⌋=100 and {100}=0. If n is the largest solution to the equation (⌊n⌋)/(n)=(2015)/(2016), compute {n}.
Original LaTeX notation
Let $\lfloor x\rfloor$ denote the largest integer less than or equal to $x$, and let $\{x\}$ denote the fractional part of $x$. For example, $\lfloor\pi\rfloor=3$, and $\{\pi\}=0.14159 \ldots$, while $\lfloor 100\rfloor=100$ and $\{100\}=0$. If $n$ is the largest solution to the equation $\frac{\lfloor n\rfloor}{n}=\frac{2015}{2016}$, compute $\{n\}$.

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Source and history

task_id
e155ca26-f068-5d4f-9e3d-7650b76e9136
task_key
test--e155ca26-f068-5d4f-9e3d-7650b76e9136
task_revision_id
1
config / split
/ test

Official source

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