List questions from ceiling-and-floor-functions

Published on 25 Mar 2026 - 14:21

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Let $f(x) = \lfloor x \lfloor x \rfloor \rfloor$ for $x \ge 0.$

Published on 01 May 2020 - 16:11

63

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How to solve ${4 \over 3} ({1 \over x} - \lfloor {1 \over x} \rfloor) = x$?

Published on 03 May 2020 - 17:36

772

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Statistics of a Gaussian random variable with the floor function transformation

Published on 06 May 2020 - 20:17

414

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How to solve $3\lfloor x \rfloor - \lfloor x^{2} \rfloor = 2\{x\}$?

Published on 10 May 2020 - 0:11

1.4k

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How to find k'th integer not divisible by n?

Published on 10 May 2020 - 16:18

81

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Evaluating $\int_{1/4}^{1/\pi}\left\lfloor\frac{2}{x}\right\rfloor \text{dx}$

Published on 13 May 2020 - 9:06

101

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Prove or disprove that there exists a number $u\geq 0$ such that $\lfloor u^n\rfloor -n$ is always even for all $n\geq 1$.

Published on 14 May 2020 - 2:17

184

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Problems with calculating the limit $\lim_{x\to \infty} \frac{1}{x}\int_0^x{\lvert \sin(t)\rvert dt}$

Published on 14 May 2020 - 14:13

210

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AIME 1991 Number theory Problem

Published on 16 May 2020 - 10:55

60

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Find the $n$th number that is not a multiple of $3,5$ or $15$

Published on 16 May 2020 - 23:51

79

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Solving equations with ceiling function

Published on 17 May 2020 - 14:13

65

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Showing that for $x > e^{2.5102}, 0 \le \lfloor\dfrac{1.25506(x+1)}{\ln(x+1)}\rfloor - \lfloor\dfrac{1.25506x}{\ln x}\rfloor \le 1$

Published on 20 May 2020 - 8:21

160

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Floor function algebra question

Published on 21 May 2020 - 3:07

195

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What is the shape/best fit equation for this curve in this image?

Published on 24 May 2020 - 7:44

List Question

Stuck with number theory identity about the divisor function

Let $f(x) = \lfloor x \lfloor x \rfloor \rfloor$ for $x \ge 0.$

How to solve ${4 \over 3} ({1 \over x} - \lfloor {1 \over x} \rfloor) = x$?

Statistics of a Gaussian random variable with the floor function transformation

How to solve $3\lfloor x \rfloor - \lfloor x^{2} \rfloor = 2\{x\}$?

How to find k'th integer not divisible by n?

Evaluating $\int_{1/4}^{1/\pi}\left\lfloor\frac{2}{x}\right\rfloor \text{dx}$

Prove or disprove that there exists a number $u\geq 0$ such that $\lfloor u^n\rfloor -n$ is always even for all $n\geq 1$.

Problems with calculating the limit $\lim_{x\to \infty} \frac{1}{x}\int_0^x{\lvert \sin(t)\rvert dt}$

AIME 1991 Number theory Problem

Find the $n$th number that is not a multiple of $3,5$ or $15$

Solving equations with ceiling function

Showing that for $x > e^{2.5102}, 0 \le \lfloor\dfrac{1.25506(x+1)}{\ln(x+1)}\rfloor - \lfloor\dfrac{1.25506x}{\ln x}\rfloor \le 1$

Floor function algebra question

What is the shape/best fit equation for this curve in this image?

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