$\left| (4 \mathbb{N} -1) \cap \mathbb{P} \right| \ = \ \infty$ where $\mathbb{P}$ is the set of prime numbers.
16621
Help understand the proof of infinitely many primes of the form $4n+3$
121273
For any prime number $p$, let $A_p$ be the set of integers $d\in \{1,2,\dots, 999\}$ s. Then what is the cardinality of $A_p$?
119180
How to prove that the set $A = \left\{ {p:{p^2} < 2,p \in {\Bbb Q^+}} \right\}$ has no greatest element?
143407
Fibonacci Numbers $F_n$ and $F_{n + 1}$ are relatively prime for all $n \geq 0$.
78356
How to prove ${n \choose p} \equiv\left\lfloor \frac{n}{p} \right\rfloor\pmod p$
106111
Understanding that there are infinitely many primes of form $4n+3$
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
44857
Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
5142
Infinitely many primes of the form $pn+1$
119051
Show that only finitely many positive integers $n$ have the property that for all $m$ for which $1<m<n$ and $\text{gcd}(m,n) = 1$, $m$ is prime.
154076
How to show this property of $\mathbb{RP}^{n}$.
30770
Prove that $C\left(\bigcup_{\alpha\in I} A_\alpha\right)=\bigcap_{\alpha\in I}C\left(A_\alpha\right)$
2218
Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]
124333
A bijection between $\mathbb{N}$ and $\mathbb{P}(\mathbb{N})$?
38860
$P(\limsup A_n)=1 $ if $\forall A \in \mathfrak{F}$ s.t. $\sum_{n=1}^{\infty} P(A \cap A_n) = \infty$