Prove: If $a^5|b^3$, then $a|b$ for integers $a, b$.
52930
Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
100426
Let $a$ and $b$ be integers. Show that if $a \equiv b \pmod{p}$ for every prime $p$, then $a = b$.
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
98963
Prove that neither $A$ nor $B$ is divisible by $5$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
85959
How do I prove that among any $5$ integers, you are able to find $3$ such that their sum is divisible by $3$?
147527
Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
80789
Prove that $\forall a,b,c,d\in \mathbb{R}\,$, $(a^2-b^2)(c^2-d^2)\leq(ac-bd)^2$ and equalities hold if and only if $ad=bc$.
139269
Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
137626
If $a,b,c$ are positive integers,and $\cfrac{a}{b}+\cfrac{b}{c}+\cfrac{c}{a}$ and $\cfrac{b}{a}+\cfrac{c}{b}+\cfrac{a}{c}$ are integers then $a=b=c$
135750
Prove that if a and b are integers, then there are unique integers q and r such that $a = bq + r$, $-|b|/2 < r \le |b|/2$
142263
Assuming $ab^2 = b^3a$ and $a^2=1$ prove that the order of $b$ is $5$.
48484
Prove that $6|a+b+c$ if and only if $6|a^3+b^3+c^3$
96153
$ x^3<y^3 \iff x<y $ proof issue.