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The Diophantine Equation $m(n-2016)=n^{2016}$
How many natural numbers, $n$, are there such that $$\frac{n^{2016}}{n-2016}$$ is a natural number?
HINT.-There are lots of solutions
HINT.-$\frac{n}{n-2016}=m \iff \frac{2016}{n-2016}=m-1$ and if, ...
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