Let $a$ and $b$ be integers $\ge 1$. prove that $(2^a-1) | (2^{ab}-1)$.
1448
$x^a - 1$ divides $x^b - 1$ if and only if $a$ divides $b$
91197
Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction
111316
PROVE if $x \ge-1 $then $ (1+x)^n \ge 1+nx $ , Every $n \ge 1$
50266
In the following figure prove that: $AK||BC$
62982
Prove $2^b-1$ does not divide $2^a + 1$ for $a,b>2$
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
118467
Prove that $a^2+ab+b^2\ge 0$
64108
how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
83662
Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
25648
Prove $(a_1+b_1)^{1/n}\cdots(a_n+b_n)^{1/n}\ge \left(a_1\cdots a_n\right)^{1/n}+\left(b_1\cdots b_n\right)^{1/n}$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
100426
Let $a$ and $b$ be integers. Show that if $a \equiv b \pmod{p}$ for every prime $p$, then $a = b$.
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
47949
If $a$ and $b$ are two roots of $x^4 + x^3 - 1 = 0$ prove that $ab$ is a root of $x^6 + x^4 + x^3 - x^2 - 1$.
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$