If $p$ is a factor of $m^2$ then $p$ is a factor of $m$
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
90811
If $[G' : G'']\leq p^2$, then $G'$ is abelian.
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
130653
$p^2$ divides $ab$ and $\gcd(a,b)=1$. Show $p^2$ divides $a$ or $p^2$ divides $b$
100984
Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
78917
Show that for any prime numbers $p,q,r$, one has $p^2+q^2 \ne r^2$.
22248
$G$ solvable $\implies$ composition factors of $G$ are of prime order.
34588
Number Theory: $p!+p=n^2$, $p$ = prime
3109
Prove that $(p+q)^m \leq p^m+q^m$
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
97652
Can every real polynomial be factored up to quadratic factors?
76644
For any odd prime $p$, a quadratic is solvable mod $p^2$ if it is solvable mod $p$, and $p$ does not divide the discriminant and leading coefficient.
49166
$R^n \cong R^m$ iff $n=m$
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$