How to prove that $8^{18} - 1$ is divisible by $7$
2522
Why is $a^n - b^n$ divisible by $a-b$?
48053
Show that 13 divides $2^{70}+3^{70}$
32166
Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$
52032
Prove that ${n^5 - n}$ is divisible by 5
122019
Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$
97911
Find all real numbers $x$ for which $\frac{8^x+27^x}{12^x+18^x}=\frac76$
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
99428
Prove that $3^{2n-1} + 2^{n+1}$ is always a multiple of $7$.
11500
Divisibility by 7 rule, and Congruence Arithmetic Laws
5358
How to prove that 2017 divides $1^{2017}+2^{2017}+\dots+2017^{2017}$?
38904
Prove that $(a + b + c)^{13}$ is divisible by $abc$ if $b|a^3$, $c|b^3$ and $a|c^3$.
91921
Divisibility of $n\cdot2^n+1$ by 3.