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1999 AMC 12 Question 30

AMC12 · 1999 AMC 12

Question 30

The number of ordered pairs of integers $(m, n)$ for which $mn \ge 0$ and

$$
m^3 + n^3 + 99mn = 33^3
$$

is equal to
  1. $2$
  2. $3$
  3. $33$
  4. $35$
  5. $99$