I have a 1024-bit number $n$ obtained by multiplying two 512-bit randomly generated prime numbers $p$ and $q$.
Then there's $\phi = (p-1)(q-1)$, which is another 1024-bit number.
I do not have $\phi$ but I do have the result obtained by multiplying $\phi$ with a random 1024-bit number.
I need to retrieve $p$ and $q$. I know how to get to $p$ and $q$ values starting from $\phi$ but I don't know how to extract $\phi$ from the product I have.
Is it even possible?