Suppose x and y are coprime integers and z is a natural number. Prove that If xy is a zth power then x and y are both zth powers.
54554
If a product of relatively prime integers is an $n$th power, then each is an $n$th power
97411
If $x^n=y^n$ and $n$ is odd then $x=y$
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
121717
Prove that $z^2 \equiv ab\pmod p$ is solvable if and only if both or neither of $x^2 \equiv a \pmod p$, $x^2 \equiv b \pmod p$ are solvable.
46383
If $x$ divides $z$, $y$ divides $z$ and $x$ and $y$ are relatively prime, then $xy$ divides $z$.
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
3820
Prove that $||x|-|y||\le |x-y|$
86211
If $x+y+z \geq xyz$ Prove that $x^2 + y^2 + z^2 \geq xyz$.
16548
Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
2614
Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
31937
How do I prove equality of x and y?
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
53801
Why are powers of coprime ideals are coprime?
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
127183
Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$