Find all positive integers $m$ with the property that every unit $a$ in $\mathbb{Z}_m$ satisfies $a^2 = 1$.
40131
If n is such that every element $(\mathbb{Z}/n\mathbb{Z})^{\times}$ is a root of $x^2-1$. Prove that $n$ divides 24.
148550
Units in quotient ring of $\mathbb Z[X]$
129163
Showing that every positive integer can be represented in this form
101345
Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...
33810
Proving there are an infinite number of pairs of positive integers $(m,n)$ such that $\frac{m+1}{n}+\frac{n+1}{m}$ is a positive integer
130027
Give a direct proof of the fact that $a^2-5a+6$ is even for any $a \in \mathbb Z$
144836
How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer?
21840
Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$
148906
Finding integers $m,n$ such that $(m-n)^2=4mn/(m+n-1)$
123482
How to compute $\mathbb{Z}_n^*$, the unit group of the integers modulo $n$?
19500
How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers
21006
Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
119360
Find all subrings of $\mathbb{Z}^2$
115244
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
93031
How to show that $\mathbb{Z}$ with the operation $m*n=m+(-1)^m n$ is associative?