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AMC 10A 2012 (Problem 22)

The sum of the first mm positive odd integers is 212 more than the sum of the first nn positive even integers. What is the sum of all possible values of nn?
(A)  255\text{(A)}\;255(B)  256\text{(B)}\;256(C)  257\text{(C)}\;257(D)  258\text{(D)}\;258(E)  259\text{(E)}\;259