Prove $2^{3^k}+1$ is a multiple of $3^k$
125618
Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction
33344
A different way to show that $a^k-1 \mid a^n-1$ if $k\mid n$?
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
51858
Showing $\gcd(2^m-1,2^n+1)=1$
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
123155
If $mn+1$ is a multiple of $24$, prove that $m+n$ is also a multiple of 24.
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
46840
How to prove that $\sum_{r=0}^n\binom{n}{r}2^r=3^n$
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
60305
Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
116175
Show that $\gcd(3k+2,5k+3)=1$
75910
Combinatorial Proof of Combinatorial Identity involving $(-1)^k \binom {n-1}{k}$
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
102524
$ 1^k+2^k+3^k+...+(p-1)^k $ always a multiple of $p$?
99428
Prove that $3^{2n-1} + 2^{n+1}$ is always a multiple of $7$.