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For any $I = [p_{n} + 2, p_{n+1}^2 - 2]$ there exists an affine function in the first quadrant that lower bounds the twin prime average counter on $I$

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#real-analysis #number-theory #prime-numbers #ceiling-and-floor-functions #twin-primes
114
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Find the largest value of $n,n\in\mathbb{I^+}$ so that this equation involving greatest integer function holds true

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#real-analysis #number-theory #elementary-number-theory #functions #ceiling-and-floor-functions
83
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Stuck on an assertion involving floors of base-$10$ logarithms

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#logarithms #ceiling-and-floor-functions
60
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A possible function for the floor function, ceiling function, and rounding function

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#summation #ceiling-and-floor-functions
175
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Alternating sum of floor/ceiling function

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#combinatorics #number-theory #summation #ceiling-and-floor-functions
74
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Doubt regarding a previously posted solution

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#number-theory #ceiling-and-floor-functions
47
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An inequality regarding the ceiling functions

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#combinatorics #number-theory #ceiling-and-floor-functions
23
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limit of log(n) over floor(log(n))

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#calculus #limits #logarithms #ceiling-and-floor-functions
55
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Given the inequalities $n > 2^k - 1$ and $n < 2^{(k+1)}$, express $k$ in terms of $n$ (where $k, n \in\Bbb N$).

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#algebra-precalculus #inequality #logarithms #ceiling-and-floor-functions #natural-numbers
49
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Determining the inverse image of $\{1,2,5\}$ under a ceiling function

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#functions #elementary-set-theory #ceiling-and-floor-functions #inverse-function
69
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Solving the following ratio of two series

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#sequences-and-series #analysis #convergence-divergence #ceiling-and-floor-functions
78
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Solving an equation involving the floor function

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#inequality #ceiling-and-floor-functions
98
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there is no integer $x \geq 2$ such that: $a+b=(a-b)x^2$

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#discrete-mathematics #arithmetic #ceiling-and-floor-functions
347
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How to solve MIT Integration Bee $2023$: $\int_0^{100} \lfloor x\rfloor x\lceil x\rceil dx$

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#integration #solution-verification #ceiling-and-floor-functions
67
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Opposite of rounding

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#ceiling-and-floor-functions

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