The complete problem is the following:

You have a set of numbers of the form M = { 7, 77, 777, ..., 77....7 (n times) }.

Can it be that you have two disjoint sets A and B such as $A \bigcup B = M$ have the property that the product of A's elements equals the product of B's elements?

Note: it's from a collection of problems for the 6th grade but I don't mind of any solution.