$m,n>1$ are relatively prime integers , then are there at-least four idempotent (w.r.t. multiplication) elements in $\mathbb Z_{mn}$ ?
7303
How many idempotent elements does the ring ${\bf Z}_n$ contain?
103147
$\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime
18018
Proving that $4 \mid m - n$ is an equivalence relation on $\mathbb{Z}$
92211
When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
140144
Can you find an element of order 10 in $\mathbb{Z}_{31}^{*}$
47186
$(1-\zeta_m)$ is a unit in $\mathbb{Z}[\zeta_m]$ if m contains at least two prime factors
31990
Is $\{\frac{m}{10^n}\mid m,n\in\mathbb Z,\ n\geq 0\}$ dense in $\mathbb R$?
4105
Irreducible but not prime in $\mathbb{Z}[\sqrt{-5}] $
45850
Prime elements in the gaussian integers
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
132725
Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
27069
sum of all positive integers less than $n$ and relatively prime to $n$
117206
$|G|$ and $|{\rm Aut}(G)|$ are relatively prime $\Rightarrow$ $G$ should be cyclic?
67208
Can we say that there exist an integer $n$ such $A+nB$ invertible?
27250
Greatest common divisor of two relatively primes
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
114404
For which positive integer values of $n$ does $a|mn-b?$