Are you sure both those posts are by the same person?
Thinking about this again. If it is possible that factorizing what c%d is congruent to (which is e) leads to c's factorization, we could set e as c', find e', set e' as c", find e" and so on until we find something that can instantly be factored (e.g. gcd(d,e)!=0). It would be recursive.
Deja vu