AMC 10B 2023 (Problem 14)

How many ordered pairs of integers (m,n)(m,n) satisfy m2+mn+n2=m2n2m^2+mn+n^2=m^2n^2?
(A)  7\text{(A)}\;7(B)  1\text{(B)}\;1(C)  3\text{(C)}\;3(D)  6\text{(D)}\;6(E)  5\text{(E)}\;5