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SMO 2013 Senior Round 1 Question 5

SMO · SMO 2013 Senior Round 1

Question 5

Find the number of integers $n$ such that the equation

$$xy^2+y^2-x-y=n$$

has an infinite number of integer solutions $(x,y)$.
  1. $0$
  2. $1$
  3. $2$
  4. $3$
  5. More than 3