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New posts in ceiling-and-floor-functions
Prove that $\frac{(3 a+3 b) !(2 a) !(3 b) !(2 b) !}{(2 a+3 b) !(a+2 b) !(a+b) ! a !(b !)^{2}}$ is an integer.
elementary-number-theory
inequality
contest-math
factorial
ceiling-and-floor-functions
About the distribution of $\{k(\sqrt{2}-1)\mid k\in \mathbb{N}\}$
summation
contest-math
problem-solving
ceiling-and-floor-functions
(floor function) sum of x: $\left\lfloor{\frac{x}{5}}\right\rfloor - \left\lfloor{\frac{x}{9}}\right\rfloor = \frac{x}{15}$
ceiling-and-floor-functions
Very challenging: max{floor,ceil}=?
calculus
ceiling-and-floor-functions
Show that $2^n<2^{\lceil n \log_23\rceil}-3^n<3^n-2^n$
limits
inequality
ceiling-and-floor-functions
collatz-conjecture
Calculation of $x$ in $x \lfloor x\lfloor x\lfloor x\rfloor\rfloor\rfloor = 88$
algebra-precalculus
ceiling-and-floor-functions
Solve the system $ x \lfloor y \rfloor = 7 $ and $ y \lfloor x \rfloor = 8 $.
contest-math
systems-of-equations
ceiling-and-floor-functions
Prove that if $x \in R,$ then there exists $n \in Z$ satisfying $x \leq n < x+1$
real-analysis
inequality
proof-explanation
ceiling-and-floor-functions
How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \lfloor\frac{\lfloor x\rfloor}{n}\rfloor=\lfloor\frac{x}{n}\rfloor$.
algebra-precalculus
proof-writing
proof-explanation
ceiling-and-floor-functions
$\lfloor x\rfloor + \lfloor y\rfloor \leq \lfloor x+y\rfloor$ for every pair of numbers of $x$ and $y$
inequality
proof-verification
ceiling-and-floor-functions
How to prove that for $a_{n+1}=\frac{a_n}{n} + \frac{n}{a_n}$ , we have $\lfloor a_n^2 \rfloor = n$?
sequences-and-series
induction
recurrence-relations
ceiling-and-floor-functions
Proof for $\left\lfloor\frac 1j\left\lfloor\frac nk\right\rfloor\right\rfloor=\left\lfloor\frac n{jk}\right\rfloor$ [duplicate]
elementary-number-theory
proof-writing
ceiling-and-floor-functions
Limit of Series with differences of Floor function
calculus
real-analysis
limits
ceiling-and-floor-functions
Show that these two numbers have the same number of digits
elementary-number-theory
logarithms
self-learning
ceiling-and-floor-functions
Limit involving floor function: $\lim\limits_{x\to 0} x \left\lfloor\frac1x \right\rfloor$ [duplicate]
calculus
limits
ceiling-and-floor-functions
Sum of $\lfloor k^{1/3} \rfloor$
sequences-and-series
summation
radicals
ceiling-and-floor-functions
How can you find the continuous digits of $g(x)=3 \lfloor x \rfloor^3$?
calculus
continuity
ceiling-and-floor-functions
Proving $\lfloor 2x \rfloor = \lfloor x \rfloor + \lfloor x+0.5\rfloor$
proof-writing
ceiling-and-floor-functions
Does $\lim_{x \to 0+} \left(x\lfloor \frac{a}{x} \rfloor\right)=a?$
calculus
real-analysis
limits
ceiling-and-floor-functions
Is true that $\sum_{k=1}^n\frac{[kx]}{k}\leq[nx]$, for every $x\in\mathbb{R}$ and for every $n\in\mathbb{Z}^+$?
number-theory
elementary-number-theory
discrete-mathematics
inequality
ceiling-and-floor-functions
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