unique integers

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November 29th 2010, 10:50 PM
mremwo

unique integers

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?

thanks!!!
November 29th 2010, 11:15 PM
aman_cc

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
November 30th 2010, 05:05 AM
HallsofIvy

Quote:

Originally Posted by mremwo

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?

thanks!!!

"Unique m and n" means there is only one pair of numbers, (m, n), that satifies the condition. It is quite possible that m and n are the same.

If you mean a pair, (m, n), such that $m^2= n$ 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.