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2014 AMC 8 Question 13

AMC8 · 2014 AMC 8

Question 13

If $n$ and $m$ are integers and $n^2 + m^2$ is even, which of the following is impossible?
  1. $n$ and $m$ are even
  2. $n$ and $m$ are odd
  3. $n + m$ is even
  4. $n + m$ is odd
  5. none of these are impossible