Prove that if $b^m$ divides $a^n$ and $m>n$, then $b$ divides $a$.
64654
Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.
55266
Prove that $(n+1)^{n-1}<n^n$
89175
Proof of $(a+b)^{n+1}$
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
83662
Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?
102757
Prove that either $m$ divides $n$ or $n$ divides $m$ given that $\operatorname{lcm}(m,n) + \operatorname{gcd}(m,n) = m + n$?
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
80144
Prove that $x-1$ divides $x^n-1$
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
31555
Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$