I'll try to make this clearer by using our math syntax. See the short intro

here:

Given \(P# = \frac{P}{P-1}\), need to find \(P##\) - original problem

We might simplify this problem by saying that this '#' sign is an operation that replaces each \(P\) with \(\frac{P}{P-1}\). \(P##\) is found by replacing all the \(P\)s with \(\frac{P}{P-1}\) in this expression:

\(\frac{P}{P-1}\), which equals \(P#\)

This is how it looks after these replacements:

\(\frac{\frac{P}{P-1}}{\frac{P}{P-1}-1}\)

Now we simplify it gradually:

\(\frac{\frac{P}{P-1}}{\frac{P}{P-1}-\frac{P-1}{P-1}}=\)

\(\frac{\frac{P}{P-1}}{\frac{P-P+1}{P-1}}=\)

\(\frac{\frac{P}{P-1}}{\frac{1}{P-1}}=\)

\(\frac{P}{P-1}*\frac{P-1}{1}=\)

\(P\)

Hope this clears the doubts.

I think that's a baldy written question. Why not P## be a multiplication? Similarly to other questions like:

Which straightly implies multiplication of the 3 numbers (as opposed to ask for a number where the 1st digit(s) would be 2^3, the next ones 4^5 and the last ones 6^7.

(Actually I got confused and ended up multiplying # * #).

In m opinion it should be written as a function (P(P#)) or something.