An integer $a \pmod m$ has inverse if and only if $\gcd(a,m)=1$?
2904
Solving linear congruence (modular inverse or fraction) via gcd Bezout equation
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
94855
Prove if a (mod n) has a multiplicative inverse, then it's unique
124279
$g^k$ is a primitive element modulo $m$ iff $\gcd (k,\varphi(m))=1$
103578
Affine cipher : Why it is required to have GCD(a, m) equals to 1
44729
Prove $g$ is a generator if $g^q=1 \pmod p$
90480
Code for (a,b) with gcd(a,b)=1?
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
62382
I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$
147079
$\gcd\left(\binom{n}{k},n\right)>1$ for nontrivial values?
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
140359
Can the sum of finitely many inverses of distinct odd integers $\geq 3$ be 1?
1576
Finding the elements in the group of units of the ring of integers modulo n that are their own inverse.
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
18108
Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$