Testing if a property belongs to all members of a set without trying each one

Assume the following assertions:

, and are positive integers.

Given and , is there a way to test that is true for all possible values of , without trying each one?

Example 1:

The set of possible values for is . is not valid because . The condition that is satisfied by all possible values of .

Example 2:

The set of possible values for is . This example does not pass the test; it fails when because:

Any help will be greatly appreciated. Thanks!

Andre

P.S. If this is not in the most appropriate thread, please direct me.