Question

Equivalent of floor division in a group of integers mod N.

score 213 · Answer 1 · 2022-04-20 15:23:58

213

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Equivalent of floor division in a group of integers mod N.

Published on 20 Apr 2022 - 15:23

score 87 · Answer 2 · 2022-04-21 21:31:25

87

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prove that $\lfloor nx \rfloor \ge \sum_{i=1}^n \frac{\lfloor xi\rfloor}{i}$.

Published on 21 Apr 2022 - 21:31

score 198 · Answer 3 · 2026-03-26 17:53:32

198

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Finding $\text{PV}\int_0^\infty\frac{\sec\left(\pi B(xt-\lfloor xt+\frac12 \rfloor\right)-\sec\left(\pi B(x-\lfloor x+\frac12 \rfloor\right)}{x}dx$

Published on 26 Mar 2026 - 17:53

score 24 · Answer 4 · 2022-04-26 16:36:22

24

Views

Approach to solve ceiling identities

Published on 26 Apr 2022 - 16:36

score 88 · Answer 5 · 2022-04-26 22:48:12

88

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How is the inequality $\displaystyle\sum_{r=1}^k\ \Big\lceil\frac{i-1}{2^r}\Big\rceil \leq i-2+k$ acquired?

Published on 26 Apr 2022 - 22:48

score 82 · Answer 6 · 2026-03-26 14:34:43

82

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Show ${\sum_{i=1}^{\frac{p-1}{2}} \lfloor \frac{2iq}{p} \rfloor + {\sum_{i=1}^{\frac{q-1}{2}}} {\lfloor \frac{2ip}{q} \rfloor}}=(p-1)/2\cdot(q-1)/2$

Published on 26 Mar 2026 - 14:34

score 43 · Answer 7 · 2022-04-29 15:04:26

43

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Proving $\frac{n}{r+\delta_1-1}\lfloor\frac{r+\delta_1-2}{r}\rfloor-\frac{n}{r+\delta_2-1}\lfloor\frac{r+\delta_2-2}{r}\rfloor\geq0$, with conditions

Published on 29 Apr 2022 - 15:04

score 148 · Answer 8 · 2022-05-05 05:28:44

148

Views

Evaluate $\int_0^1 \left(\{ax\}-\frac{1}{2}\right)\left(\{bx\}-\frac{1}{2}\right) dx$ for $a,b\in\mathbb{Z}^+$

Published on 05 May 2022 - 5:28

score 337 · Answer 9 · 2026-03-28 17:41:19

337

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Formulas of Mellin inversion theorem that involve Riemann zeta function $\zeta (s)$ and floor function $\lfloor x\rfloor$

Published on 28 Mar 2026 - 17:41

score 32 · Answer 10 · 2022-05-13 03:04:11

32

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> Estimation of number of distinct integers in the sequence $a_i =\lfloor \frac{n}{n + 1 - i} \rfloor, i\geq 0$ for some given $n$

Published on 13 May 2022 - 3:04

score 343 · Answer 11 · 2026-03-28 00:06:05

343

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Recursive analytic continuation of Riemann zeta function

Published on 28 Mar 2026 - 0:06

score 99 · Answer 12 · 2026-03-29 06:47:37

99

Views

Solve for x: $\lfloor x\rfloor \{\sqrt{x}\}=1$ where $\{x\}=x-\lfloor x\rfloor$

Published on 29 Mar 2026 - 6:47

score 80 · Answer 13 · 2026-03-27 21:19:25

80

Views

Is $(1+c^2)^n-\lfloor(1+c^2)^{n/2}\rfloor^2<(1+c^2)^{(n+1)/2}$ true for all integers $c>1$, when $n$ is an odd integer?

Published on 27 Mar 2026 - 21:19

score 395 · Answer 14 · 2026-03-29 06:47:37

395

Views

Find $\int_1^\infty \frac{\{x\}}{x(x+1)}dx,$ where $\{x\}$ means $x - \lfloor x \rfloor$.

Published on 29 Mar 2026 - 6:47

score 45 · Answer 15 · 2022-05-26 20:01:48

45

Views

How to prove that $ \sum_{n=1}^{\infty} \frac{(-1)^{[\log n]}}{n}$ diverges?

Published on 26 May 2022 - 20:01

List Question

Equivalent of floor division in a group of integers mod N.

prove that $\lfloor nx \rfloor \ge \sum_{i=1}^n \frac{\lfloor xi\rfloor}{i}$.

Finding $\text{PV}\int_0^\infty\frac{\sec\left(\pi B(xt-\lfloor xt+\frac12 \rfloor\right)-\sec\left(\pi B(x-\lfloor x+\frac12 \rfloor\right)}{x}dx$

Approach to solve ceiling identities

How is the inequality $\displaystyle\sum_{r=1}^k\ \Big\lceil\frac{i-1}{2^r}\Big\rceil \leq i-2+k$ acquired?

Show ${\sum_{i=1}^{\frac{p-1}{2}} \lfloor \frac{2iq}{p} \rfloor + {\sum_{i=1}^{\frac{q-1}{2}}} {\lfloor \frac{2ip}{q} \rfloor}}=(p-1)/2\cdot(q-1)/2$

Proving $\frac{n}{r+\delta_1-1}\lfloor\frac{r+\delta_1-2}{r}\rfloor-\frac{n}{r+\delta_2-1}\lfloor\frac{r+\delta_2-2}{r}\rfloor\geq0$, with conditions

Evaluate $\int_0^1 \left(\{ax\}-\frac{1}{2}\right)\left(\{bx\}-\frac{1}{2}\right) dx$ for $a,b\in\mathbb{Z}^+$

Formulas of Mellin inversion theorem that involve Riemann zeta function $\zeta (s)$ and floor function $\lfloor x\rfloor$

> Estimation of number of distinct integers in the sequence $a_i =\lfloor \frac{n}{n + 1 - i} \rfloor, i\geq 0$ for some given $n$

Recursive analytic continuation of Riemann zeta function

Solve for x: $\lfloor x\rfloor \{\sqrt{x}\}=1$ where $\{x\}=x-\lfloor x\rfloor$

Is $(1+c^2)^n-\lfloor(1+c^2)^{n/2}\rfloor^2<(1+c^2)^{(n+1)/2}$ true for all integers $c>1$, when $n$ is an odd integer?

Find $\int_1^\infty \frac{\{x\}}{x(x+1)}dx,$ where $\{x\}$ means $x - \lfloor x \rfloor$.

How to prove that $ \sum_{n=1}^{\infty} \frac{(-1)^{[\log n]}}{n}$ diverges?

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