Prove that any base $a>1$ , each positive integer $m$ has a unique expression of the form $a^nr_n+a^{n-1}r_{n-1}+...+ar_1+r_0$
56528
On the proof of existence and uniqueness of radix representation
44100
Prove that identity element is unique
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
2614
Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$
102817
$A,B\in M_{n}(\mathbb{R})$ so that $A>0, B>0$, prove that $\det (A+B)>\max (\det(A), \det(B))$
63182
For every $n \ge 1$ there exist uniquely determined integers $a \gt 0$ and $b \gt 0$ such that $n = a^2b$ where $b$ is square-free.
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
145397
How to prove that for every $i$, $a_i = i$
48503
Proving : $ \bigl(1+\frac{1}{n+1}\bigr)^{n+1} \gt (1+\frac{1}{n})^{n} $
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
93031
How to show that $\mathbb{Z}$ with the operation $m*n=m+(-1)^m n$ is associative?
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
16660
Prove that any positive number has an $n$th root
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers
107824
Proof by induction that $a_0 = 1, a_1 = 1, a_n=2a_{n-1} + 3a_{n-2}$ satisfies $a_n = \frac12 (3^n) + \frac12 (-1)^n$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$