Question

Solving a tough equation involving integer functions

score 84 · Answer 1 · 2019-02-25 11:24:05

84

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Solving a tough equation involving integer functions

Published on 25 Feb 2019 - 11:24

score 96 · Answer 2 · 2019-02-27 12:16:21

96

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Calculate the derivative $f(x)=\lfloor x\rfloor(\sin(\pi x))^{2}$

Published on 27 Feb 2019 - 12:16

score 202 · Answer 3 · 2019-02-28 09:19:39

202

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Find $\lim\limits_{x\to0^+}x(\lfloor \frac{1}{x}\rfloor+\lfloor \frac{2}{x}\rfloor+\cdots+\lfloor \frac{k}{x}\rfloor), \, k \in \mathbb N$.

Published on 28 Feb 2019 - 9:19

score 83 · Answer 4 · 2019-03-01 12:48:06

83

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How to prove $\lceil \log_2{(n+1)} - 1 \rceil \ge \lfloor \log_2(n) \rfloor$?

Published on 01 Mar 2019 - 12:48

score 123 · Answer 5 · 2019-03-03 11:34:20

123

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Prove that if $p$ is a prime number, then p divides $\binom{n}{p} − \lfloor\frac{n}{p}\rfloor$, for all $n > p$.

Published on 03 Mar 2019 - 11:34

score 670 · Answer 6 · 2019-03-05 00:27:29

670

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Finding and proving a closed form formula for a recursive formula with floor and ceiling functions

Published on 05 Mar 2019 - 0:27

score 81 · Answer 7 · 2019-03-06 06:43:27

81

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A doubt about greatest integer function

Published on 06 Mar 2019 - 6:43

score 650 · Answer 8 · 2019-03-06 09:09:43

650

Views

Calculate the sum $S_n = \sum\limits_{k=1}^{\infty}\left\lfloor \frac{n}{2^k} + \frac{1}{2}\right\rfloor $

Published on 06 Mar 2019 - 9:09

score 59 · Answer 9 · 2019-03-06 10:37:21

59

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Finding bounds on $g$ if $g(\frac{n}{2})=n\frac{m}{2}-\left[\lceil \frac{nm}{m+1}\rceil-\lceil\frac1{2}\lceil\frac{n}{m}\rceil\right]m$

Published on 06 Mar 2019 - 10:37

score 244 · Answer 10 · 2019-03-06 11:22:43

244

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Find range of $x$ satisfying $\left \lfloor \frac{3}{x} \right \rfloor+\left \lfloor \frac{4}{x} \right \rfloor=5$

Published on 06 Mar 2019 - 11:22

score 214 · Answer 11 · 2019-03-07 01:04:40

214

Views

Floor function of sum of square roots

Published on 07 Mar 2019 - 1:04

score 132 · Answer 12 · 2026-03-25 09:25:19

132

Views

Reasoning with fractional parts and the Möbius function.

Published on 25 Mar 2026 - 9:25

score 158 · Answer 13 · 2019-03-09 19:31:21

158

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Find sum $ \sum\limits_{k=2}^{2^{2^n}} \frac{1}{2^{\lfloor \log_2k \rfloor} \cdot 4^{\lfloor \log_2(\log_2k )\rfloor}} $

Published on 09 Mar 2019 - 19:31

score 72 · Answer 14 · 2019-03-13 17:08:46

72

Views

Calculate the floor-function of the expression

Published on 13 Mar 2019 - 17:08

score 39 · Answer 15 · 2019-03-14 00:04:47

39

Views

Let $n$ be an integer, prove that $\lfloor n/2 \rfloor \geq (n-1)/2$

Published on 14 Mar 2019 - 0:04

List Question

Solving a tough equation involving integer functions

Calculate the derivative $f(x)=\lfloor x\rfloor(\sin(\pi x))^{2}$

Find $\lim\limits_{x\to0^+}x(\lfloor \frac{1}{x}\rfloor+\lfloor \frac{2}{x}\rfloor+\cdots+\lfloor \frac{k}{x}\rfloor), \, k \in \mathbb N$.

How to prove $\lceil \log_2{(n+1)} - 1 \rceil \ge \lfloor \log_2(n) \rfloor$?

Prove that if $p$ is a prime number, then p divides $\binom{n}{p} − \lfloor\frac{n}{p}\rfloor$, for all $n > p$.

Finding and proving a closed form formula for a recursive formula with floor and ceiling functions

A doubt about greatest integer function

Calculate the sum $S_n = \sum\limits_{k=1}^{\infty}\left\lfloor \frac{n}{2^k} + \frac{1}{2}\right\rfloor $

Finding bounds on $g$ if $g(\frac{n}{2})=n\frac{m}{2}-\left[\lceil \frac{nm}{m+1}\rceil-\lceil\frac1{2}\lceil\frac{n}{m}\rceil\right]m$

Find range of $x$ satisfying $\left \lfloor \frac{3}{x} \right \rfloor+\left \lfloor \frac{4}{x} \right \rfloor=5$

Floor function of sum of square roots

Reasoning with fractional parts and the Möbius function.

Find sum $ \sum\limits_{k=2}^{2^{2^n}} \frac{1}{2^{\lfloor \log_2k \rfloor} \cdot 4^{\lfloor \log_2(\log_2k )\rfloor}} $

Calculate the floor-function of the expression

Let $n$ be an integer, prove that $\lfloor n/2 \rfloor \geq (n-1)/2$

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