If $a^2$ divides $b^2$, then $a$ divides $b$
10236
Show that $a^n \mid b^n$ implies $a \mid b$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
19202
$\mathbb{F}_{p^d}\subseteq\mathbb{F}_{p^n}$ if and only if $d$ divides $n$
48404
If $a$ and $b$ are integers such that $9$ divides $a^2 + ab + b^2$ then $3$ divides both $a$ and $b$.
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
85449
Show a,b,c congruences when $a^2+b^2=c^2$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
134365
When is this true: If $m^2$ is a multiple of N then m is a multiple of N
84733
Why $a\equiv b\pmod n$ implies $a$ and $b$ have equal remainder when divided by $n$?
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 $a=b$?
4396
If $A^2\succ B^2$, then necessarily $A\succ B$
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
118809
If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c
142133
Prove that if $a^2 + b^2 = c^2$, then 5 divides abc. a,b,c are positive integers.
96027
Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite.
64654
Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.