Prove that $\nu(n) \le \nu(2^{n}-1)$ where $\nu(n)$ is the number of positive divisors of n
139383
Prove that $\tau(2^n-1) \geq \tau(n)$ for all positive integers $n$.
149056
Prove that for all $n\geqslant 1$ we have $F_n<{\left(\frac 74\right)}^n$.
34017
Show that $n^{\pi\left(2n\right)-\pi\left(n\right)}2$
16253
Proof that $|\sin(nx)| \le n|\sin(x)|$
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
76696
Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$
68561
How to show $\lceil ( \sqrt3 +1)^{2n}\rceil$ where $n \in \mathbb{ N}$ is divisible by $2^{n+1}$
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
55266
Prove that $(n+1)^{n-1}<n^n$
133528
$\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$
42976
How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
148330
Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$