List questions from fractional-part

Published on 25 Jun 2019 - 14:25

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Prove $⌊2x⌋+⌊2y⌋≥⌊x⌋+⌊y⌋+⌊x+y⌋$

Published on 24 Mar 2026 - 6:27

270

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Let $F_1$ and $F_2$ be the fractional parts of $(44-\sqrt 2017)^{2017}$ and $(44+ \sqrt 2017)^{2017}$ respectively. Then $F_1+F_2$ lies between?

Published on 01 Aug 2019 - 17:04

46

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If matrix $A=[a_{ij}]_{4 \times 4}$ such that...

Published on 21 Aug 2019 - 20:27

53

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If $\{x\}:=x-\lfloor x\rfloor$, then are these the same? $\{l+m\}$, $\left\{l+\{m\}\right\}$, $\left\{\left\{l\right\}+\{m\}\right\}$

Published on 23 Aug 2019 - 20:51

145

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Is fractional part of $e^n$ dense in (0,1)?

Published on 25 Aug 2019 - 1:55

135

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Prove that $\left|\left\{\frac{n}{1}\right\} - \left\{\frac{n}{2}\right\} - \cdots - (-1)^n\left\{\frac{n}{n}\right\}\right| \le \sqrt{2n}$.

Published on 06 Sep 2019 - 16:42

183

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Evaluate the limit $\lim\limits_{n\to0}\frac{(x)+(2x)+\cdots (nx)}{n^2}$

Published on 23 Feb 2026 - 21:16

48

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Find number of x such that $\{x\}+\{x^2\}=1,x\in(0,20). $Where $\{\}$ denotes fractional part.

Published on 26 Sep 2019 - 19:08

64

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Relations between $\sqrt x$ and $\sqrt{x+n}$

Published on 08 Apr 2014 - 19:48

4.2k

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Irrational fractional parts - patterns

Published on 29 Apr 2014 - 6:55

80

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Verify my proof on elementary number theory

Published on 17 May 2014 - 23:52

1.2k

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limit involving sine of fractional part

Published on 11 Jun 2014 - 8:48

12.2k

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How to find out the period of fractional part of x

Published on 21 Jun 2014 - 4:52

6k

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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 22 Jun 2014 - 16:58

List Question

fractional imaginary calculation

Prove $⌊2x⌋+⌊2y⌋≥⌊x⌋+⌊y⌋+⌊x+y⌋$

Let $F_1$ and $F_2$ be the fractional parts of $(44-\sqrt 2017)^{2017}$ and $(44+ \sqrt 2017)^{2017}$ respectively. Then $F_1+F_2$ lies between?

If matrix $A=[a_{ij}]_{4 \times 4}$ such that...

If $\{x\}:=x-\lfloor x\rfloor$, then are these the same? $\{l+m\}$, $\left\{l+\{m\}\right\}$, $\left\{\left\{l\right\}+\{m\}\right\}$

Is fractional part of $e^n$ dense in (0,1)?

Prove that $\left|\left\{\frac{n}{1}\right\} - \left\{\frac{n}{2}\right\} - \cdots - (-1)^n\left\{\frac{n}{n}\right\}\right| \le \sqrt{2n}$.

Evaluate the limit $\lim\limits_{n\to0}\frac{(x)+(2x)+\cdots (nx)}{n^2}$

Find number of x such that $\{x\}+\{x^2\}=1,x\in(0,20). $Where $\{\}$ denotes fractional part.

Relations between $\sqrt x$ and $\sqrt{x+n}$

Irrational fractional parts - patterns

Verify my proof on elementary number theory

limit involving sine of fractional part

How to find out the period of fractional part of x

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

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