Let #X be defined as X^2 + 4 for all values X. If #P = #(P + 3), what is the value of P ?

Could you please explain, how the # function is working. Since I am educated
in a non-american jurisdiction, I've never encountered such a function.
Thanks in advance

You are probably familiar with the f(x) notation for a function. Essentially, a function is a machine where you substitute values in for the variable, x, and the machine delivers some value. Of course, the formal definition is a bit more complex than the latter, but for GMAT purposes, this is enough.

Lets look at the problem #x can be taken to be f(x) = x² + 4. So that means #p = p(x) = p² + 4
and #(p + 3) = (p + 3)² + 4. Now, lets set the last two equal to each other:

#p = #(p + 3) =>

p² + 4 = (p + 3)² + 4
p² + 4 = (p² + 6p + 9) + 4
p² + 4 = p² + 6p + 13
6p = -9
p = -3/2