Question

Evaluating $\lfloor (3 + \sqrt{5})^{34} \rfloor \pmod {100}$

score 363 · Answer 1 · 2014-05-25 01:48:27

363

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Evaluating $\lfloor (3 + \sqrt{5})^{34} \rfloor \pmod {100}$

Published on 25 May 2014 - 1:48

score 168 · Answer 2 · 2014-06-01 01:52:30

168

Views

Values of $n$ for which $\lfloor 2 x\rfloor +\lfloor 4 x\rfloor +\lfloor 8 x\rfloor +\lfloor 20 x\rfloor =n$ has a solution

Published on 01 Jun 2014 - 1:52

score 28 · Answer 3 · 2014-06-01 06:11:40

28

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How to find the minima for $y = x^2 + a.x - \lfloor\sqrt{x^2+a.x - b}\rfloor^2$?

Published on 01 Jun 2014 - 6:11

score 1.4k · Answer 4 · 2014-06-04 17:10:16

1.4k

Views

Expectation of a floor function applied to a continuous uniform random variable

Published on 04 Jun 2014 - 17:10

score 85 · Answer 5 · 2014-06-05 10:31:53

85

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Proof for $\sum_{x=1}^{n-1}\left\lfloor \dfrac{mx}{n}\right\rfloor=\dfrac{(n-1)(m-1)}{2}$ where $(m,n)=1$

Published on 05 Jun 2014 - 10:31

score 77 · Answer 6 · 2014-06-05 10:44:54

77

Views

Divisibility of $\lfloor (1+\sqrt{3})^{2m+1}\rfloor$ by $2^k$

Published on 05 Jun 2014 - 10:44

score 110 · Answer 7 · 2014-06-05 11:16:48

110

Views

Prove that $\lceil \frac{\sqrt{n^2+1+\sqrt{n^2}}}{\sqrt{n^2+3+\sqrt{n^2+2}}-\sqrt{n^2+2+\sqrt{n^2+1}}}\rceil = 2n^2+n+3$

Published on 05 Jun 2014 - 11:16

score 4k · Answer 8 · 2014-06-11 09:15:17

4k

Views

limits involving greatest integer function

Published on 11 Jun 2014 - 9:15

score 426 · Answer 9 · 2014-06-21 14:14:15

426

Views

Polynomial equal to the ceiling of x

Published on 21 Jun 2014 - 14:14

score 6k · Answer 10 · 2026-03-25 10:57:20

6k

Views

For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$

Published on 25 Mar 2026 - 10:57

score 374 · Answer 11 · 2014-06-23 10:17:47

374

Views

How to derive this inequality?

Published on 23 Jun 2014 - 10:17

score 183 · Answer 12 · 2014-06-24 10:59:55

183

Views

A problem of sum floors

Published on 24 Jun 2014 - 10:59

score 365 · Answer 13 · 2014-06-24 16:00:11

365

Views

Number of solutions to equation involving floor-function

Published on 24 Jun 2014 - 16:00

score 1.3k · Answer 14 · 2014-06-25 14:46:25

1.3k

Views

Algebraic manipulation of floors and ceilings

Published on 25 Jun 2014 - 14:46

score 297 · Answer 15 · 2014-07-01 20:47:35

297

Views

Floor Function Bound?

Published on 01 Jul 2014 - 20:47

List Question

Evaluating $\lfloor (3 + \sqrt{5})^{34} \rfloor \pmod {100}$

Values of $n$ for which $\lfloor 2 x\rfloor +\lfloor 4 x\rfloor +\lfloor 8 x\rfloor +\lfloor 20 x\rfloor =n$ has a solution

How to find the minima for $y = x^2 + a.x - \lfloor\sqrt{x^2+a.x - b}\rfloor^2$?

Expectation of a floor function applied to a continuous uniform random variable

Proof for $\sum_{x=1}^{n-1}\left\lfloor \dfrac{mx}{n}\right\rfloor=\dfrac{(n-1)(m-1)}{2}$ where $(m,n)=1$

Divisibility of $\lfloor (1+\sqrt{3})^{2m+1}\rfloor$ by $2^k$

Prove that $\lceil \frac{\sqrt{n^2+1+\sqrt{n^2}}}{\sqrt{n^2+3+\sqrt{n^2+2}}-\sqrt{n^2+2+\sqrt{n^2+1}}}\rceil = 2n^2+n+3$

limits involving greatest integer function

Polynomial equal to the ceiling of x

For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$

How to derive this inequality?

A problem of sum floors

Number of solutions to equation involving floor-function

Algebraic manipulation of floors and ceilings

Floor Function Bound?

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