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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.

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The hint.

Use $2023=7\cdot17^2$, $16=17-1$ and the binomial of Newton.

Now we see that $16^{2023}+1$ is divisible even by $17^3$.

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