better you post the problem - it would make the context clear, and a lot of times answer to what you have asked follows from there
what exactly does it mean for integers to be unique? if i am supposed to prove that there exists UNIQUE positive m and n integers under a condition, can m and n be equal at some conditions? for them to be unique, does it just mean there is only one m and only one n each time the condition is met? as in if xsqrd= m, there would not be a unique solution m?
If you mean a pair, (m, n), such that then, no, that would not be unique- but not just because, for example, both of (-2, 4) and (2, 4) is such a pair. It is also not unique because (2, 4) and (3, 9) are such pairs.