Prove that for a given prime $p$ and each $0 < r < p-1$, there exists a $q$ such that $rq \equiv 1 \bmod p$
31917
If $q$ is coprime to $a$ then $a\mid nq-1,\,$ so $q$ is invertible mod $a$
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
83407
How to show that that $q \mid p-1$?
26478
Show that the congruence $x^{p-1} \equiv 1 \pmod {p^2}$ has precisely $p-1$ solutions modulo $p^2$
146053
Proving identities (mod $pq$) using Fermat's little theorem?
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
122741
$x^2$ is congruent to $-1 \bmod p$
81346
Let $r$ be the smallest positive integer such that $a^r \equiv 1 \bmod{n}$. Prove $r \mid \phi(n)$.
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
122326
Proving $|P(A\cap B)-P(A)P(B)|\leq \frac{1}4$
125868
Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.
88036
Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$
116585
$r$ primitive root of prime $p$, where $p \equiv 1 \mod 4$: prove $-r$ is also a primitive root
140830
Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$