Prove that $\lfloor \log_{10}(xy)\rfloor \geq \lfloor \log_{10}(x)\rfloor+ \lfloor \log_{10}(y)\rfloor$
138316
A simple inequality for floor function
1840
How can I prove that $\log^k(n) = O(n^\epsilon)$?
140409
Prove that $\sqrt{n} > \ln n$
5914
Proving $\lfloor 2x \rfloor = \lfloor x \rfloor + \lfloor x+0.5\rfloor$
121694
How to prove $\log n \leq \sqrt n$ over natural numbers?
157898
Showing that $\sum_{i=1}^n \frac{1}{i} \geq \log{n}$
59462
Prove that $n!=\prod_{k=1}^n \operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)$ for any $n \in \mathbb N$
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
138819
Prove that $\phi(n) \geq \sqrt{n}/2$
115799
Proving $x^{\log n} = n^{\log x}$
27844
How do we prove that $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$?
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
71394
Prove the following floor function identity
152311
Proving expression$\geq 2$, where variables are $x,y,z$
133505
Let $f(n)=\sum_{k=0}^{\left\lfloor n/2\right\rfloor} {2k \choose k}{n \choose 2k}$ . Show that $\sum_{n\geq 0}^{} f(n)x^n=\frac{1}{\sqrt{1-2x-3x^2}}$
156831
Prove $\Sigma_{k=0}^{n-1}\lfloor x+\frac{k}{n}\rfloor=\lfloor nx\rfloor$ , n is a Natural Number