Modulo Arithmetic/Examples/11 Divides 3^3n+1 + 2^2n+3

Example of Modulo Arithmetic

 * $11$ is a divisor of $3^{3 n + 1} + 2^{2 n + 3}$.

Proof
We have:

Now:

Then we have:

and:

So:

Hence:
 * $\forall n \in \N: 11 \divides \paren {3^{3 n + 1} + 2^{4 n + 3} }$