Show that if $x$ is a primitive root modulo $p^r$, then $x$ is a primitive root modulo $p$
2614
Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$
81778
If $m|n$ and $a$ is a primitive root of $n$, show that $a$ is a primitive root of $m$ (understanding a tip)
120627
Reducibility of polynomials modulo p
103323
Finding a primitive root of a prime number
120629
Prove if $n$ has a primitive root, then it has exactly $\phi(\phi(n))$ of them
23153
$\bmod p\!:\ x^2\equiv 1\iff x\equiv \pm1\ $ for prime $p$
21466
$P$ is projective . Show that $P$ is a direct summand of a free $R-$ module
41693
Use irreducible fibers to show $X$ is irreducible
77820
Roots in a polynomial ring
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
83050
Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
116686
$p=2^n+1$. Prove that every quadratic nonresidue modulo $p$ is a primitive root modulo $p$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
134916
When g and -g are both primitive roots
79535
Prove that $R$ is a commutative ring if $x^3=x$
115241
If $p$ and $q = 2p + 1$ are both odd primes, show that $-4$ and $2(-1)^{(1/2)(p-1)}$ are both primitive roots modulo $q$.