Question

Floors Complicated Proof

score 155 · Answer 1 · 2017-04-30 21:25:55

155

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Floors Complicated Proof

Published on 30 Apr 2017 - 21:25

score 284 · Answer 2 · 2017-05-01 17:20:29

284

Views

Nested ceiling simplification

Published on 01 May 2017 - 17:20

score 53 · Answer 3 · 2017-05-06 15:26:06

53

Views

Proof that $f : \mathbb{R} \rightarrow [0,1]$ with $f(x) = x−\lfloor x\rfloor$ is bijective

Published on 06 May 2017 - 15:26

score 81 · Answer 4 · 2017-05-09 16:10:27

81

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How to prove this property involving the floor function?

Published on 09 May 2017 - 16:10

score 496 · Answer 5 · 2026-03-26 13:52:14

496

Views

Prove that $\lim\limits_{k\to\infty}\left(\frac1k\sum\limits_{n=1}^k\left\lfloor\frac kn\right\rfloor-\ln k\right)=2\gamma-1$

Published on 26 Mar 2026 - 13:52

score 187 · Answer 6 · 2026-03-25 22:30:42

187

Views

Convergence of the limit of a series involving Möbius and Floor functions

Published on 25 Mar 2026 - 22:30

score 213 · Answer 7 · 2026-03-25 22:05:12

213

Views

Prove that $\forall a\in \mathbb{R\smallsetminus Q}$, there exist infinitely many $n\in \mathbb N$ such that $\lfloor{an^2}\rfloor$ is even.

Published on 25 Mar 2026 - 22:05

score 87 · Answer 8 · 2017-05-12 13:18:26

87

Views

Integral of the floor function. Can anyone prove the following identity?

Published on 12 May 2017 - 13:18

score 204 · Answer 9 · 2026-03-30 16:46:44

204

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Find integer part of the maximum value of $x^4y+x^3y+x^2y+xy+xy^2+xy^3+xy^4$ for $x+y=3$

Published on 30 Mar 2026 - 16:46

score 259 · Answer 10 · 2026-04-01 17:05:38

259

Views

Definite integral involving Greatest Integer Function and arcsec(x) & arccot(x)

Published on 01 Apr 2026 - 17:05

score 57 · Answer 11 · 2017-05-21 08:49:24

57

Views

Proof $\sum_{k=1}^{p-1}\left\lfloor\dfrac{km}{p}\right\rfloor=\dfrac{(m-1)(p-1)}{2}$ with $m$ and $p$ co-prime numbers

Published on 21 May 2017 - 8:49

score 116 · Answer 12 · 2017-05-23 12:49:53

116

Views

Analytic number theory question.

Published on 23 May 2017 - 12:49

score 236 · Answer 13 · 2017-05-27 15:51:51

236

Views

Solutions of $\lfloor 2x \rfloor \times \lfloor 3x \rfloor + \lfloor 4x \rfloor=0$

Published on 27 May 2017 - 15:51

score 94 · Answer 14 · 2017-05-30 03:07:13

94

Views

Evaluation of Finite Product Involving Ceiling Function

Published on 30 May 2017 - 3:07

score 451 · Answer 15 · 2017-06-02 12:49:16

451

Views

Sum of first n natural numbers, each multiplied by an irrational constant and floored

Published on 02 Jun 2017 - 12:49

List Question

Floors Complicated Proof

Nested ceiling simplification

Proof that $f : \mathbb{R} \rightarrow [0,1]$ with $f(x) = x−\lfloor x\rfloor$ is bijective

How to prove this property involving the floor function?

Prove that $\lim\limits_{k\to\infty}\left(\frac1k\sum\limits_{n=1}^k\left\lfloor\frac kn\right\rfloor-\ln k\right)=2\gamma-1$

Convergence of the limit of a series involving Möbius and Floor functions

Prove that $\forall a\in \mathbb{R\smallsetminus Q}$, there exist infinitely many $n\in \mathbb N$ such that $\lfloor{an^2}\rfloor$ is even.

Integral of the floor function. Can anyone prove the following identity?

Find integer part of the maximum value of $x^4y+x^3y+x^2y+xy+xy^2+xy^3+xy^4$ for $x+y=3$

Definite integral involving Greatest Integer Function and arcsec(x) & arccot(x)

Proof $\sum_{k=1}^{p-1}\left\lfloor\dfrac{km}{p}\right\rfloor=\dfrac{(m-1)(p-1)}{2}$ with $m$ and $p$ co-prime numbers

Analytic number theory question.

Solutions of $\lfloor 2x \rfloor \times \lfloor 3x \rfloor + \lfloor 4x \rfloor=0$

Evaluation of Finite Product Involving Ceiling Function

Sum of first n natural numbers, each multiplied by an irrational constant and floored

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