Divisibility of $a^x - 1$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
129647
$A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$
91921
Divisibility of $n\cdot2^n+1$ by 3.
280
Prove by induction that $5^n - 1$ is divisible by $4$.
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
149576
$x(a^{1/x}-1)$ is decreasing
116363
If $P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x)$ , then prove that $P(x)$ is divisible by $x-1$
962
divisibility problem using induction
153892
Number Theory divisibilty
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
116970
On the number divisors of a number
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
64148
If $p$ and $q$ are distinct primes and $a$ be any integer then $a^{pq} -a^q -a^p +a$ is divisible by $pq$.
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
74523
Proof by Cases involving divisibility