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 prove that $a=b$ -Struck
71012
If $a, b$ are positive integers such that $a|b^2, b^2|a^3,....$ then $a=b$.
50614
If $4\mid a+bc$ and $6\mid b+ac$ prove that $2\mid a^2-b^2$
95588
Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
116215
Prove that $P(A \cap B\mid C)=P(A \mid (B \cap C))P(B\mid C)$
10236
Show that $a^n \mid b^n$ implies $a \mid b$
138846
Prove by induction that $3\mid n^4-n^2$ for all $n \in \mathbb{Z^+}$, $n\ge2$.
78985
Prove that: $\sqrt{2\sqrt{3\sqrt{4\cdots\sqrt{n}}}}<3,\,\forall n\in\mathbb N.$
114404
For which positive integer values of $n$ does $a|mn-b?$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
156541
$a^b > b^a$ or $a^b b$ where $a,b$ are positive real numbers
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
133699
Proving that there is a bijection between $A$ and $B$.
17677
Prove or show a counter example for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$
83721
If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.