Prove by induction that $\forall n \in \mathbb{N}^*$ we have that $2^{2^n} + 3^{2^n} + 5^{2^n} \equiv 0 \pmod{19}$.
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction