Let
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
be a composite natural number and
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
a proper divisor of
![n.](/media/m/4/7/8/478d25bfe04800537ae6e85be9d11ea2.png)
Find the binary representation of the smallest natural number
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
such that
is an integer.
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Let $n$ be a composite natural number and $p$ a proper divisor of $n.$ Find the binary representation of the smallest natural number $N$ such that
$$\frac{(1 + 2^p + 2^{n-p})N - 1}{2^n}$$
is an integer.