Editing Znám's problem (section)

==The problem==
Znám's problem asks which sets of integers have the property that each integer in the set is a [[proper divisor]] of the product of the other integers in the set, plus 1. That is, given <math>k</math>, what sets of integers 
<math display=block>\{n_1, \ldots, n_k\}</math>
are there such that, for each <math>i</math>, <math>n_i</math> divides but is not equal to
<math display=block>\Bigl(\prod_{j \ne i}^n n_j\Bigr) + 1 ?</math>
A closely related problem concerns sets of integers in which each integer in the set is a divisor, but not necessarily a proper divisor, of one plus the product of the other integers in the set. This problem does not seem to have been named in the literature, and will be referred to as the improper Znám problem. Any solution to Znám's problem is also a solution to the improper Znám problem, but not necessarily vice versa.