Starting with the equation:
$\frac{1}{a}+\frac{1}{b}=\frac{p}{10^n}$,
I reached the equation:
$10^{n-log(p)} = \frac{ab}{a+b}$.
Now given the positive integer $n$, for what integer values of $p$ would the value of:
$10^{n-log(p)}$,
be rational?
Also, given positive integers $n$ and $p$, how would we find positive integer solutions to $a$ and $b$ that satisfy the second equation, where:
$a ≤ b$,
And is it possible to determine, given $n$ and $p$, how many $a$ and $b$ solutions exist?