If AM-GM holds for any $2^n$ positive real numbers, show that AM-GM holds for *any number* of positive real numbers.
13228
Proofs of AM-GM inequality
74486
How to understand Cauchy's proof of AM-GM inequality(the last step)
1305
Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
130093
Prove by Induction : $n < 2^n$
42567
Let $(a_n)_{n \geq 0}$ be a strictly decreasing sequence of positive real numbers , and let $z \in \mathbb C$ , $|z| < 1$.
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
43940
Showing that $n$ is pseudoprime to the base $a$
90670
Prove $a^ab^bc^c\ge (abc)^{\frac{a+b+c}3}$ for positive numbers.
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
11127
Let $a$, $b$, and $c$ be positive real numbers.
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
70006
$a,b,m,n$ be positive integers such that g.c.d.$(a,b)=1$ and $a^m+b^m|a^n+b^n$ , then $m|n$?
96217
If a and b are non-negative real numbers then demonstrate inequality
20438
Prove that every positive integer $n$ has a unique expression of the form: $2^{r}m$ where $r\ge 0$ and $m$ is an odd positive integer
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
2554
Show that if $n>2$, then $(n!)^2>n^n$.