Suppose [unparseable or potentially dangerous latex formula], [unparseable or potentially dangerous latex formula] are integers whose greatest common divisor is [unparseable or potentially dangerous latex formula]. Let [unparseable or potentially dangerous latex formula] be a set of integers with the following properties:
(a) For [unparseable or potentially dangerous latex formula].
(b) For [unparseable or potentially dangerous latex formula] (not necessarily distinct), [unparseable or potentially dangerous latex formula]
(c) For any integers [unparseable or potentially dangerous latex formula], if [unparseable or potentially dangerous latex formula], then [unparseable or potentially dangerous latex formula]
Prove that [unparseable or potentially dangerous latex formula] must be equal to the set of all integers.