Question

For positive real $a$, $b$ with $a+b<1$, prove or disprove that there exists natural $n$ such that $\{na\}+\{nb\}\geq1$

score 1.1k · Answer 1 · 2012-01-30 07:03:30

1.1k

Views

For positive real $a$, $b$ with $a+b<1$, prove or disprove that there exists natural $n$ such that $\{na\}+\{nb\}\geq1$

Published on 30 Jan 2012 - 7:03

score 1.4k · Answer 2 · 2026-04-01 20:04:44

1.4k

Views

How do we prove that $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$?

Published on 01 Apr 2026 - 20:04

score 7.4k · Answer 3 · 2012-03-08 01:07:43

7.4k

Views

Proof of greatest integer theorem: floor function is well-defined

Published on 08 Mar 2012 - 1:07

score 1.1k · Answer 4 · 2012-03-15 10:21:54

1.1k

Views

Find all real numbers $x$ satisfying $[x+2]=6[x] -23$

Published on 15 Mar 2012 - 10:21

score 112 · Answer 5 · 2012-04-03 20:52:50

112

Views

Simple question about the ceiling function

Published on 03 Apr 2012 - 20:52

score 3.4k · Answer 6 · 2012-05-24 14:16:48

3.4k

Views

How to solve an equation involving the floor of a number?

Published on 24 May 2012 - 14:16

score 299 · Answer 7 · 2012-06-02 08:28:07

299

Views

Getting an upper bound for a function of two variables

Published on 02 Jun 2012 - 8:28

score 1.2k · Answer 8 · 2012-07-19 12:09:38

1.2k

Views

Proving $\left\lfloor \frac{x}{ab} \right\rfloor = \left\lfloor \frac{\left\lfloor \frac{x}{a} \right\rfloor}{b} \right\rfloor$ for $a,b>1$

Published on 19 Jul 2012 - 12:09

score 13.7k · Answer 9 · 2012-08-19 18:41:57

13.7k

Views

Floor function properties: $[2x] = [x] + [ x + \frac12 ]$ and $[nx] = \sum_{k = 0}^{n - 1} [ x + \frac{k}{n} ] $

Published on 19 Aug 2012 - 18:41

score 329 · Answer 10 · 2012-09-03 19:00:33

329

Views

When does $\lfloor (n-1)x \rfloor + \lfloor x \rfloor = \lfloor nx \rfloor$?

Published on 03 Sep 2012 - 19:00

score 250 · Answer 11 · 2012-09-08 05:53:46

250

Views

The value of $\bigl\lfloor x\bigr\rfloor+\bigl\lfloor x^2\bigr\rfloor+\bigl\lfloor x^3\bigr\rfloor+\bigl\lfloor x^4\bigr\rfloor$

Published on 08 Sep 2012 - 5:53

score 133 · Answer 12 · 2012-10-27 03:33:58

133

Views

Writing $f(c)=2^{\lfloor \frac{c}{10} \rfloor}c$ without floor function

Published on 27 Oct 2012 - 3:33

score 198 · Answer 13 · 2012-10-30 23:46:04

198

Views

solve for $f(x)$ in $4\lfloor\frac{x}{3}\rfloor - f(x) - 3\lfloor\frac{x-3f(x)}{9}\rfloor=x$

Published on 30 Oct 2012 - 23:46

score 215 · Answer 14 · 2012-11-27 23:39:19

215

Views

Is there a way to rewrite $L = \left\lceil \frac{\sqrt{v-4 \times N}-1}{4} \right\rceil$ without the ceiling function?

Published on 27 Nov 2012 - 23:39

score 384 · Answer 15 · 2026-03-31 20:54:09

384

Views

Theta bound about $\sum \lfloor {\sqrt{n}}\rfloor$

Published on 31 Mar 2026 - 20:54

List Question

For positive real $a$, $b$ with $a+b<1$, prove or disprove that there exists natural $n$ such that $\{na\}+\{nb\}\geq1$

How do we prove that $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$?

Proof of greatest integer theorem: floor function is well-defined

Find all real numbers $x$ satisfying $[x+2]=6[x] -23$

Simple question about the ceiling function

How to solve an equation involving the floor of a number?

Getting an upper bound for a function of two variables

Proving $\left\lfloor \frac{x}{ab} \right\rfloor = \left\lfloor \frac{\left\lfloor \frac{x}{a} \right\rfloor}{b} \right\rfloor$ for $a,b>1$

Floor function properties: $[2x] = [x] + [ x + \frac12 ]$ and $[nx] = \sum_{k = 0}^{n - 1} [ x + \frac{k}{n} ] $

When does $\lfloor (n-1)x \rfloor + \lfloor x \rfloor = \lfloor nx \rfloor$?

The value of $\bigl\lfloor x\bigr\rfloor+\bigl\lfloor x^2\bigr\rfloor+\bigl\lfloor x^3\bigr\rfloor+\bigl\lfloor x^4\bigr\rfloor$

Writing $f(c)=2^{\lfloor \frac{c}{10} \rfloor}c$ without floor function

solve for $f(x)$ in $4\lfloor\frac{x}{3}\rfloor - f(x) - 3\lfloor\frac{x-3f(x)}{9}\rfloor=x$

Is there a way to rewrite $L = \left\lceil \frac{\sqrt{v-4 \times N}-1}{4} \right\rceil$ without the ceiling function?

Theta bound about $\sum \lfloor {\sqrt{n}}\rfloor$

Trending Questions

Popular # Hahtags

Popular Questions