# Prove that $16 ^ {2023} + 1$ is divisible by $17 ^ 2$.

Prove that $$16 ^ {2023} + 1$$ is divisible by $$17 ^ 2$$.

It is clear that $$16 ^ {2023} + 1$$ is divisible by $$17$$, but why it is divisible by $$17 ^ 2$$ is not clear.

Use $$2023=7\cdot17^2$$, $$16=17-1$$ and the binomial of Newton.
Now we see that $$16^{2023}+1$$ is divisible even by $$17^3$$.