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we can write $$2^{16} - 1$$ as $$16^4 - 1^4$$
and we know $$a^n - b^n$$ is always divisible by (a-b) and (a+b) if n is even hence
$$16^4 - 1^4$$ will always be divisible by (16-1) and (16+1) and hence the answer is 17
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