we have m^3+n^3+99mn=33^3

find the number of pairs of integers (m,n) for which mn>=0

well, i see that LHS is the expansion of:

(m+n)^3=m^3+3(m+n)mn+n^3

so m+n=33 or m=0 and n=0
we have a total of 34 solutions ie (0,33),(1,32),...,(33,0)

but its a multiple choice question with solutions A)2 B) 3 C)33 D)35 E)99

its driving me crazy that my answer is between 33 and 35!! what am i missing?