Prove that $3^{2n-1} + 2^{n+1}$ is divisible by $7$ for all values of $n$
99428
Prove that $3^{2n-1} + 2^{n+1}$ is always a multiple of $7$.
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
117167
$3^{n+1}$ divides $2^{3^n}+1$
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
105854
Prove $n^2(n^4-1)$ is divisible by 60 using Mathematical Induction.
6561
Prove that the expression $5^{2n+1} \cdot 2^{n+2} + 3^{n+2} \cdot 2^{2n+1}$ is divisible by 19.
11500
Divisibility by 7 rule, and Congruence Arithmetic Laws
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
125040
Show by induction : $n^7-n$ is a multiple of 7
30620
For which natural n is $3^n+5^n$ divisible by $3^{n-1}+5^{n-1}$?
89175
Proof of $(a+b)^{n+1}$
1837
Showing that $1^k+2^k + \dots + n^k$ is divisible by $n(n+1)\over 2$
82774
Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
144132
The number $2^{3^n}+1$ is divisible by $3^{n+1}$ and not divisible by $3^{n+2}$.
55266
Prove that $(n+1)^{n-1}<n^n$
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$