Let $A=3^{105} + 4^{105}$. Show that $7\mid A$.
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
111295
Prove that $a^7 + b^7 + c^7 \geq a^4b^3 + b^4c^3 + c^4a^3$
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
100450
Prove that 3 is a primitive root of $7^k$ for all $k \ge 1$
30583
If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
78416
Show that $7$ divides $a^{15}-a^3$ for any integer $a$
100613
Prove that if an average of a thousand numbers is less than 7, then at least one of the numbers being averaged is less than 7
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
127293
Prove that $(a-b) \mid (a^n-b^n)$
33344
A different way to show that $a^k-1 \mid a^n-1$ if $k\mid n$?
90283
Proof that $3 \mid \left( a^2+b^2 \right)$ iff $3 \mid \gcd \left( a,b\right)$
118574
prove that $24 \mid a(a^2-1)$
133819
How to prove that $364 \mid n^{91} - n^7$?
77579
Proof by induction that $ 169 \mid 3^{3n+3}-26n-27$
48053
Show that 13 divides $2^{70}+3^{70}$
12210
Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
97666
Prove $133\mid \left(11^{n+2}+12^{2n+1}\right)$