If $n$ is not prime, can $X^{n-1}+\dotsb+X+1$ be irreducible?
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
46292
Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$
114480
Example of a domain where all irreducibles are primes and that is not a GCD domain
8977
Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible
88656
For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$
37315
not both $2^n-1,2^n+1$ can be prime.
16592
Irreducible polynomial which is reducible modulo every prime
29572
Proof that $2^n-1$ does not always generate primes when primes are plugged in for $n$?
9787
Primitive roots modulo primes congruent to n!
135102
How do the definitions of "irreducible" and "prime" elements differ?
127205
Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$
41693
Use irreducible fibers to show $X$ is irreducible
93291
Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
101882
Does this polynomial evaluate to prime number whenever $x$ is a natural number?
79208
Is the number $-1$ prime?
46951
For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$?
140006
Are there infinitely many primes and non primes of the form $10^n+1$?