Prove or disprove if ma ≡ mb (mod n), then a ≡ b (mod n) for all positive integers a, b, m, n.
99815
Dividing versus multiplying by inverse in modular arithmetic
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
77383
Prove that $n^3=n \text{ mod }6$ for every integer $n$.
90438
To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
27544
With $a,\ b,\ m,\ n\in \mathbb{Z}$. Show that if ${\rm gcd}(m,n)=1$, then ${\rm gcd}(ma+nb,mn)={\rm gcd}(a,n){\rm gcd}(b,m)$
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
122612
An integer is a $n$'th power if that holds true for all moduli.
100426
Let $a$ and $b$ be integers. Show that if $a \equiv b \pmod{p}$ for every prime $p$, then $a = b$.
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
17176
Proof that $x^n \mod b = (x \mod b)^n$
156966
Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
63769
Group theory proof of Euler's theorem ($a^{\phi(m)} \equiv 1\mbox{ }(\mbox{mod }m)$ if $\gcd(a,m)=1$)
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
86030
Prove or disprove - If a divides b and b divides a does a=b
91451
find all positive integer $m,n$
134365
When is this true: If $m^2$ is a multiple of N then m is a multiple of N