List questions from ceiling-and-floor-functions

Published on 21 Apr 2021 - 14:57

119

Views

Finding $\sum_{k=1}^{p-1}\left\lfloor\frac {k^3}{p} \right\rfloor $

Published on 21 Apr 2021 - 17:09

453

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If $x$ lies between $3$ and $5$, $5$ inclusive, what is the probability that $\lfloor x^2\rfloor = \lfloor x\rfloor^2?$

Published on 22 Apr 2021 - 17:15

107

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How many positive real numbers $x\le 2000$ exist such that $x\cdot \left\{ x \right\}=17$?

Published on 22 Apr 2021 - 20:39

225

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Prove that $\sum_{k=0}^{n-1}\left \lfloor x+\dfrac{k}{n}\right \rfloor=\lfloor nx\rfloor$

Published on 23 Apr 2021 - 23:39

103

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Periodic function and greatest integral function

Published on 04 Apr 2026 - 3:47

79

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How to prove the equality of the floors of two expressions?

Published on 24 Apr 2021 - 19:09

163

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Will the limit exist?

Published on 28 Apr 2021 - 14:06

499

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Continuity in greatest integer function

Published on 30 Apr 2021 - 21:10

117

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For positive integer $n$, why is $\lfloor \log_{10}(2^n)\rfloor + \lfloor \log_{10}(5^n)\rfloor + 2 = n+1$?

Published on 07 May 2021 - 3:07

169

Views

What is the clearest way of proving of $[x]+[x+1/2]=[2x]$?

Published on 11 May 2021 - 18:09

50

Views

Infinitely recursive summation of floor function

Published on 28 Mar 2026 - 22:25

37

Views

Solution verification of a series with integer part

Published on 16 May 2021 - 17:19

89

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Find the solution of $x^2-4=[x]$

Published on 29 Mar 2026 - 5:06

191

Views

Condition that satisfies inequality involving fractions and the floor function

Published on 18 May 2021 - 14:32

List Question

Trying to solve an equation involving the floor function for an algorithm

Finding $\sum_{k=1}^{p-1}\left\lfloor\frac {k^3}{p} \right\rfloor $

If $x$ lies between $3$ and $5$, $5$ inclusive, what is the probability that $\lfloor x^2\rfloor = \lfloor x\rfloor^2?$

How many positive real numbers $x\le 2000$ exist such that $x\cdot \left\{ x \right\}=17$?

Prove that $\sum_{k=0}^{n-1}\left \lfloor x+\dfrac{k}{n}\right \rfloor=\lfloor nx\rfloor$

Periodic function and greatest integral function

How to prove the equality of the floors of two expressions?

Will the limit exist?

Continuity in greatest integer function

For positive integer $n$, why is $\lfloor \log_{10}(2^n)\rfloor + \lfloor \log_{10}(5^n)\rfloor + 2 = n+1$?

What is the clearest way of proving of $[x]+[x+1/2]=[2x]$?

Infinitely recursive summation of floor function

Solution verification of a series with integer part

Find the solution of $x^2-4=[x]$

Condition that satisfies inequality involving fractions and the floor function

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