List questions from ceiling-and-floor-functions

Published on 18 Feb 2023 - 16:41

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Simplifying floor function summation $\sum^m_{k=0} \left(\left\lfloor{\frac{n}{m}k}\right\rfloor-\left\lceil{\frac{n}{m}(k-1)}\right\rceil\right)$

Published on 27 Feb 2023 - 15:23

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Hint with floors and ceiling proof

Published on 02 Mar 2023 - 4:03

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Solving $\lfloor {2x} \rfloor + \lceil {x} \rceil - 4x = 0$

Published on 02 Mar 2023 - 22:03

102

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Does this summation span all natural numbers?

Published on 02 Mar 2023 - 22:26

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Conjecture $ \sum _{i=1}^{n-1}\lfloor \frac{i^2}{n}\rfloor \ge \frac{\left(n-1\right)\left(n-2\right)}3$ where $n\in\mathbb N^*$

Published on 07 Mar 2023 - 13:13

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How to evaluate $\int_0^{2\pi} [|\sin(x)| + |\cos(x)|]\ dx $ where $[.]$ denotes greatest integer function

Published on 09 Mar 2023 - 13:06

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Sum of floor logarithm function

Published on 10 Mar 2023 - 4:50

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Is $a \lceil \frac b c \rceil \geq \lceil \frac {ab} c \rceil$? ($a, b \geq 0$ and $c > 0$)

Published on 10 Mar 2023 - 18:29

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Figuring out best lower bound for Leetcode #2187. Minimum Time to Complete Trips

Published on 28 Mar 2026 - 20:40

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Algebraic manipulation in summations involving the floor function

Published on 25 Mar 2026 - 8:21

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What triplets satisfy this condition using floors?

Published on 18 Mar 2023 - 20:58

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Integral of the square of a floor function in an infinite sum

Published on 23 Mar 2023 - 5:49

183

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Prove or disprove that $\gcd\left(n!+1,f\left(n\right)\right)=1$

Published on 24 Mar 2023 - 7:23

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Using algebra to figure out how many boxes fit in an area without over estimating

Published on 26 Mar 2026 - 14:30

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Proving inequality with multiple gaussian brackets

Simplifying floor function summation $\sum^m_{k=0} \left(\left\lfloor{\frac{n}{m}k}\right\rfloor-\left\lceil{\frac{n}{m}(k-1)}\right\rceil\right)$

Hint with floors and ceiling proof

Solving $\lfloor {2x} \rfloor + \lceil {x} \rceil - 4x = 0$

Does this summation span all natural numbers?

Conjecture $ \sum _{i=1}^{n-1}\lfloor \frac{i^2}{n}\rfloor \ge \frac{\left(n-1\right)\left(n-2\right)}3$ where $n\in\mathbb N^*$

How to evaluate $\int_0^{2\pi} [|\sin(x)| + |\cos(x)|]\ dx $ where $[.]$ denotes greatest integer function

Sum of floor logarithm function

Is $a \lceil \frac b c \rceil \geq \lceil \frac {ab} c \rceil$? ($a, b \geq 0$ and $c > 0$)

Figuring out best lower bound for Leetcode #2187. Minimum Time to Complete Trips

Algebraic manipulation in summations involving the floor function

What triplets satisfy this condition using floors?

Integral of the square of a floor function in an infinite sum

Prove or disprove that $\gcd\left(n!+1,f\left(n\right)\right)=1$

Using algebra to figure out how many boxes fit in an area without over estimating

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