Question

Help verify the proof that $\min \left({\lfloor{N/2}\rfloor, \lfloor{(N + 2)/p}\rfloor}\right) = \lfloor{(N + 2)/p}\rfloor$ for $N \ge p$

score 129 · Answer 1 · 2016-12-20 23:01:46

129

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Help verify the proof that $\min \left({\lfloor{N/2}\rfloor, \lfloor{(N + 2)/p}\rfloor}\right) = \lfloor{(N + 2)/p}\rfloor$ for $N \ge p$

Published on 20 Dec 2016 - 23:01

score 54 · Answer 2 · 2026-03-25 23:37:02

54

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Proving a particular inequality between two sums of ceiling

Published on 25 Mar 2026 - 23:37

score 78 · Answer 3 · 2026-03-25 18:56:24

78

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Density function for ${frac(\frac{N}{i})}_{i=1}^{i=N}$ in the limit $N \to \infty$

Published on 25 Mar 2026 - 18:56

score 124 · Answer 4 · 2016-12-27 13:57:23

124

Views

Proof of Number Theoretic Function $\sigma$

Published on 27 Dec 2016 - 13:57

score 133 · Answer 5 · 2016-12-27 16:26:45

133

Views

Inequality with floor function

Published on 27 Dec 2016 - 16:26

score 373 · Answer 6 · 2016-12-27 18:39:20

373

Views

Explicit solution of the recursion $x_n = x_{n-1}^2 - 2$ with $x_0>2$

Published on 27 Dec 2016 - 18:39

score 156 · Answer 7 · 2016-12-29 22:35:13

156

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How to solve the equation $3x-4\lfloor x\rfloor=0$ for $x\in\mathbb{R}$?

Published on 29 Dec 2016 - 22:35

score 144 · Answer 8 · 2016-12-30 11:17:44

144

Views

Calculate limit with floor function or prove it doesnt exist

Published on 30 Dec 2016 - 11:17

score 1.7k · Answer 9 · 2016-12-31 01:36:03

1.7k

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Replacing floor operation with modulus

Published on 31 Dec 2016 - 1:36

score 998 · Answer 10 · 2017-01-02 06:28:00

(floor function) sum of x: $\left\lfloor{\frac{x}{5}}\right\rfloor - \left\lfloor{\frac{x}{9}}\right\rfloor = \frac{x}{15}$

score 101 · Answer 11 · 2017-01-02 17:14:18

101

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Let $f(x) = x + \left[ x \right]$. What is ${f^{ - 1}}(x)$?

Published on 02 Jan 2017 - 17:14

score 106 · Answer 12 · 2026-03-25 18:57:52

106

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Prove that $\lfloor x + y + z \rfloor = \lfloor x + y \rfloor + \lfloor z + \langle y + x \rangle \rfloor$

Published on 25 Mar 2026 - 18:57

score 277 · Answer 13 · 2017-01-04 07:58:11

277

Views

Solving for inverse-functions involving $[x]$ and $\{x\}$

Published on 04 Jan 2017 - 7:58

score 957 · Answer 14 · 2017-01-04 14:57:00

957

Views

Induction with floor, ceiling $n\le2^k\implies a_n\le3\cdot k2^k+4\cdot2^k-1$ for $a_n=a_{\lfloor\frac{n}2\rfloor}+a_{\lceil\frac{n}2\rceil}+3n+1$

Published on 04 Jan 2017 - 14:57

score 71 · Answer 15 · 2017-01-04 19:46:17

71

Views

Plot $f(\lfloor x \rfloor)$ using $f(x)$

Published on 04 Jan 2017 - 19:46

List Question

Help verify the proof that $\min \left({\lfloor{N/2}\rfloor, \lfloor{(N + 2)/p}\rfloor}\right) = \lfloor{(N + 2)/p}\rfloor$ for $N \ge p$

Proving a particular inequality between two sums of ceiling

Density function for ${frac(\frac{N}{i})}_{i=1}^{i=N}$ in the limit $N \to \infty$

Proof of Number Theoretic Function $\sigma$

Inequality with floor function

Explicit solution of the recursion $x_n = x_{n-1}^2 - 2$ with $x_0>2$

How to solve the equation $3x-4\lfloor x\rfloor=0$ for $x\in\mathbb{R}$?

Calculate limit with floor function or prove it doesnt exist

Replacing floor operation with modulus

(floor function) sum of x: $\left\lfloor{\frac{x}{5}}\right\rfloor - \left\lfloor{\frac{x}{9}}\right\rfloor = \frac{x}{15}$

Let $f(x) = x + \left[ x \right]$. What is ${f^{ - 1}}(x)$?

Prove that $\lfloor x + y + z \rfloor = \lfloor x + y \rfloor + \lfloor z + \langle y + x \rangle \rfloor$

Solving for inverse-functions involving $[x]$ and $\{x\}$

Induction with floor, ceiling $n\le2^k\implies a_n\le3\cdot k2^k+4\cdot2^k-1$ for $a_n=a_{\lfloor\frac{n}2\rfloor}+a_{\lceil\frac{n}2\rceil}+3n+1$

Plot $f(\lfloor x \rfloor)$ using $f(x)$

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