Show that $t^n-1 \mid t^m-1 \Leftrightarrow n\mid m$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
54427
$\left|x_{n+1} - x_n\right| < C\left|x_n - x_{n-1}\right|$ prove this is Cauchy
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
145423
prove that if $1 \le m \le n$ then $\left(1+\frac1n\right)^m < 1+\frac mn + \left(\frac mn\right)^2$
23071
Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$
127293
Prove that $(a-b) \mid (a^n-b^n)$
20467
Show that $(y_n)\in l^q$
98017
If $a_{n+1}/a_n\to\ell$ show $a_n^{1/n}\to\ell$
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
142928
Proving $\left\{ \frac{1}{n} \right\}$ is Cauchy
18018
Proving that $4 \mid m - n$ is an equivalence relation on $\mathbb{Z}$
149056
Prove that for all $n\geqslant 1$ we have $F_n<{\left(\frac 74\right)}^n$.
18914
How prove this $A=\left(B-\frac{1}{110}I\right)^T\left(B+\frac{1}{110}I\right)$
10236
Show that $a^n \mid b^n$ implies $a \mid b$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
55266
Prove that $(n+1)^{n-1}<n^n$