Prove that if $m$ divide $n$ then $x^{p^{m-1}}-1$ divide $x^{p^{n-1}}-1$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
85525
Prove that $x^3+x+1$ splits in $Z_2[x]/(x^3+x+1)$
145423
prove that if $1 \le m \le n$ then $\left(1+\frac1n\right)^m < 1+\frac mn + \left(\frac mn\right)^2$
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
34323
Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
3109
Prove that $(p+q)^m \leq p^m+q^m$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
117167
$3^{n+1}$ divides $2^{3^n}+1$
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
31555
Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)