Is it true for every prime power $q$ that $q-1 | q^r - 1$?
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
134963
Proving a non-prime (composite) number $> 1$ has a divisor $d \leq\sqrt q$
111037
Consider numbers of the type $n=2^m+1$. Prove that such an n is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime.
131551
$pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes
144814
If $p$ and $q$ are primes, which binomial coefficients $\binom{pq}{n}$ are divisible by $pq$?
8710
Bounds for $n$-th prime
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
113763
Let $p$,$\ q$ be prime numbers and $n\in \mathbb{N}$ such that $p \nmid n-1$. If $p \mid n^q-1$, then $q \mid p-1$.
77806
Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
6869
The square roots of different primes are linearly independent over the field of rationals
42932
Prove that $p^j q^i$ cannot be a perfect number for $p, q$ odd, distinct primes.
59391
$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
86594
If $x^2 \equiv y^2 \pmod {p^r}$, where $p$ is an odd prime not dividing $x$ or $y$ then $x \equiv \pm y \pmod {p^r}$
68221
Question regardles primes and the fundamental theorem of arithmetic
82097
If $A \succeq B$, is it true that $B^{-1} \succeq A^{-1}$?