Is it true that for every $p$ and $q$ prime there exist infinitely many $k$ such that $p^k - 1$ is divisible by $q$?
123219
What is multiplicative group $\bar{\mathbb{F}}_p^*$ for algebraic closure $\bar{\mathbb{F}}_p$ of $\mathbb{F}_p$ where $p$ is prime?
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 $q \mid p-1$.
140830
Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$
68221
Question regardles primes and the fundamental theorem of arithmetic
52530
There exists a prime congruent to $m$ mod $p$
158106
Prove that 1 less than the number of equivalence classes divides $p-1$ where $p$ is prime
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$
138409
Proof of infinitely many primes, clarification
35821
Infinitely many primes for quadratic residues
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
131289
Polynomial with a root modulo every prime but not in $\mathbb{Q}$.
42932
Prove that $p^j q^i$ cannot be a perfect number for $p, q$ odd, distinct primes.
65131
Can infinitely many primes lie over a prime?
50596
$p_1p_2...p_n +1$ is not square for $p_k = k$'th prime
69830
How often is $1+\prod_{k=1}^n p_k$ not prime?
94174
Ring of polynomials over a field has infinitely many primes