If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
112147
Proving $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
29963
$6$ divides $a+b+c$ if and only if $6$ divides $a^{3}+b^{3}+c^{3}$
66558
Find the value of $a$ and $b$ if $x+1$ and $x−2$ are factors of $ax^3−4x^2+bx−12$
55437
When does $2^{n}$ divide $3^{n}-1$
38904
Prove that $(a + b + c)^{13}$ is divisible by $abc$ if $b|a^3$, $c|b^3$ and $a|c^3$.
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
1991
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
87522
If $ a + b + c \mid a^2 + b^2 + c^2$ then $ a + b + c \mid a^n + b^n + c^n$ for infinitely many $n$
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 $a=b$?
106847
Proof that $n^3+2n$ is divisible by $3$
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
1448
$x^a - 1$ divides $x^b - 1$ if and only if $a$ divides $b$