Can the knowledge of the inverse of $p$ modulo $q$ help factor $n=pq$?
This question was already answered in this not-so-great titled question.

($p$ and $q$ being "safe primes" does not matter in this context, but $q$ shouldn't be (much) longer than $p$, as the methods works for $q&lt;p$, but can be adapted by "guessing" the top bits of $q$ otherwise).