I've seen a number of job openings that ask for this. The difference between m and n can be substantial.
Why would a company do this?
Is it to get the hopes up of a potential applicant, and then offer something that's still in the range, but lower than the top?
Will they pay more if they find a superstar, and change the position's requirements to give them more responsibilities?
Or do they simply not know what they want?
Surely they already know what the job entails, and how much they're willing to pay for it. If they're presumably accepting the best candidate out of a hundred possible applicants, why wouldn't they always offer n?