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?
The set of possible values for is . is not valid because . The condition that is satisfied by all possible values of .
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!
P.S. If this is not in the most appropriate thread, please direct me.
Thank you very much for your helpful response. My confusion arose from the ceiling function in .
You've helped me realize the obvious solution for all because for all where .
Still, the other parts of the problem, namely the declaration that , serve to impose a limit on such that can be satisfied when .
I don't yet understand if there is a way to test that can be satisfied given and , short of trying each member of the set of all possible values for .
Discovering a solution to the full problem is less important for me now that I know we can easily prove it for all , which is enough for most practical applications in computer science.