Show that $12n+5$ and $5n-2$ are relatively prime for all $n$ (in $\mathbb{Z}$)
6943
Idea behind proof that $\frac{21n+4}{14n+3}$ is irreducible for all $n$
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
4105
Irreducible but not prime in $\mathbb{Z}[\sqrt{-5}] $
32278
Adjoining 1/2 to $\Bbb{Z}/12\Bbb{Z}$
118452
how to prove $\mathbb Z_n$ has divisors of zero if and only if $n$ is not prime
147101
Show that if $p>5$ is prime, then $240 \mid (p^4-1)$
12365
Show that every prime $p>3$ is either of the form $6n+1$ or of the form $6n+5$
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.
27069
sum of all positive integers less than $n$ and relatively prime to $n$
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
83935
Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$
63702
There is a prime between $n$ and $n^2$, without Bertrand
135892
Understanding the proof for showing that there are infinitely many $n\in\mathbb{Z}^+$ such that $n!+1$ is divisible by at least two distinct primes
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
76807
How come if $\ i\ $ not of the following form, then $12i + 5$ must be prime?
15348
prime divisor of $3n+2$ proof
50995
infinitude of primes that are $11 \bmod 12$