Question

Largest possible difference between "round numbers" (multiples of powers of 10) that contain a given interval

score 35 · Answer 1 · 2024-01-11 19:25:57

35

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Largest possible difference between "round numbers" (multiples of powers of 10) that contain a given interval

Published on 11 Jan 2024 - 19:25

score 95 · Answer 2 · 2024-01-14 13:00:02

95

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Solve for $x>0, \sqrt{x+\lfloor x\rfloor}+\sqrt{x+\{x\}}=\sqrt{x+\lfloor x\rfloor\{x\}}+\sqrt{x+1}$

Published on 14 Jan 2024 - 13:00

score 112 · Answer 3 · 2026-02-24 02:02:29

112

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Reasonable and Logical Integration

Published on 24 Feb 2026 - 2:02

score 136 · Answer 4 · 2024-01-17 10:41:26

136

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Show that $\int_0^1 \left \lbrace (-1)^{\left \lceil \frac{1}{x} \right \rceil }\frac{1}{x} \right \rbrace \, {\rm d}x = \frac{\pi}{2}$

Published on 17 Jan 2024 - 10:41

score 89 · Answer 5 · 2024-01-21 08:00:35

89

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Evaluate $\int_0^1(\sum_{n=0}^\infty \frac{[2^n x]}{3^n})^2$ where [.] represent the greatest integer fn.

Published on 21 Jan 2024 - 8:00

score 51 · Answer 6 · 2024-01-22 02:09:31

51

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Greatest Integer Function Equality

Published on 22 Jan 2024 - 2:09

score 243 · Answer 7 · 2024-01-26 03:53:46

243

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Geometric interpretation of Hermite's identity

Published on 26 Jan 2024 - 3:53

score 362 · Answer 8 · 2024-01-28 12:03:35

362

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$z_2+z_3+z_4+z_5=n$ satisfing $i\not\mid z_i$

Published on 28 Jan 2024 - 12:03

score 173 · Answer 9 · 2026-03-25 21:49:40

173

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What is $\int\limits_0^1\left\{\frac{1}{x\left\{\frac{1}{x}\right\}}\right\}dx$?

Published on 25 Mar 2026 - 21:49

score 109 · Answer 10 · 2024-02-03 16:07:52

109

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For any $N \in \mathbb{N}$ there exist integers $x,y,z>N$ such that $\{\sqrt{x}\}+\{\sqrt{y}\}=1+\{\sqrt{z}\}$

Published on 03 Feb 2024 - 16:07

score 113 · Answer 11 · 2026-03-30 11:59:24

113

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Does $\prod\limits_{n=1}^{\infty}\int\limits_{-1}^{1}\left|\frac{\lfloor t^{1-n}\rfloor}{\lfloor t^{-n}\rfloor}\right|dt$ converge to $1$?

Published on 30 Mar 2026 - 11:59

score 116 · Answer 12 · 2026-03-25 21:47:59

116

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Solutions to $\left\{x^n\right\}=\{x\}^n$

Published on 25 Mar 2026 - 21:47

score 56 · Answer 13 · 2024-02-06 18:13:53

56

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Is $\lceil x \rceil=\frac{1}{2}(1+ \sum_{n=-\infty}^{+\infty}(\operatorname{sgn}(x-n)-|\operatorname{sgn}(x-n)|+1+\operatorname{sgn}(n)))$ true?

Published on 06 Feb 2024 - 18:13

score 105 · Answer 14 · 2024-02-07 14:59:00

105

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For a discrete moving point, find its first coordinates where it lies in a circle

Published on 07 Feb 2024 - 14:59

score 179 · Answer 15 · 2024-02-08 03:14:04

179

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Closed form of $\displaystyle\sum_{k=1}^n\sum_{j=1}^k\left\lfloor\dfrac{(j-1)^2}{m}\right\rfloor$

Published on 08 Feb 2024 - 3:14

List Question

Largest possible difference between "round numbers" (multiples of powers of 10) that contain a given interval

Solve for $x>0, \sqrt{x+\lfloor x\rfloor}+\sqrt{x+\{x\}}=\sqrt{x+\lfloor x\rfloor\{x\}}+\sqrt{x+1}$

Reasonable and Logical Integration

Show that $\int_0^1 \left \lbrace (-1)^{\left \lceil \frac{1}{x} \right \rceil }\frac{1}{x} \right \rbrace \, {\rm d}x = \frac{\pi}{2}$

Evaluate $\int_0^1(\sum_{n=0}^\infty \frac{[2^n x]}{3^n})^2$ where [.] represent the greatest integer fn.

Greatest Integer Function Equality

Geometric interpretation of Hermite's identity

$z_2+z_3+z_4+z_5=n$ satisfing $i\not\mid z_i$

What is $\int\limits_0^1\left\{\frac{1}{x\left\{\frac{1}{x}\right\}}\right\}dx$?

For any $N \in \mathbb{N}$ there exist integers $x,y,z>N$ such that $\{\sqrt{x}\}+\{\sqrt{y}\}=1+\{\sqrt{z}\}$

Does $\prod\limits_{n=1}^{\infty}\int\limits_{-1}^{1}\left|\frac{\lfloor t^{1-n}\rfloor}{\lfloor t^{-n}\rfloor}\right|dt$ converge to $1$?

Solutions to $\left\{x^n\right\}=\{x\}^n$

Is $\lceil x \rceil=\frac{1}{2}(1+ \sum_{n=-\infty}^{+\infty}(\operatorname{sgn}(x-n)-|\operatorname{sgn}(x-n)|+1+\operatorname{sgn}(n)))$ true?

For a discrete moving point, find its first coordinates where it lies in a circle

Closed form of $\displaystyle\sum_{k=1}^n\sum_{j=1}^k\left\lfloor\dfrac{(j-1)^2}{m}\right\rfloor$

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