Proof that if $a^3 \mid b^2$ then $a\mid b$.
52930
Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
56878
Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
49548
If $(a + ib)^3 = 8$, prove that $a^2 + b^2 = 4$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
130488
Prove by induction that $3\mid n^3 - n$
13914
If $a^2+b^2=c^2$ then $a$ or $b$ is even.
11693
If $p \mid m^p+n^p$ prove $p^2 \mid m^p+n^p$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
46286
Prove if $a\mid b$ and $b\mid a$, then $|a|=|b|$ , $a, b$ are integers.
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
39175
Prove by induction that $\forall n \in\mathbb N$, $3\mid4^{n}-1$.
12100
$n \mid (a^{n}-b^{n}) \ \Longrightarrow$ $n \mid \frac{a^{n}-b^{n}}{a-b}$
58133
${a^2}{\mid}({b^3} + 1)\;$and$\;{b^2}{\mid}({a^3} + 1)$