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SMO 2006 Junior Round 1 Question 8

SMO · SMO 2006 Junior Round 1

Question 8

Suppose that only one of the following pairs $(x,y)$ yields the positive integer $\sqrt{x^2+y^2}$. Then which pair is it?
  1. $x=25530,\ y=29464$
  2. $x=37615,\ y=26855$
  3. $x=15123,\ y=32477$
  4. $x=28326,\ y=28614$
  5. $x=22536,\ y=27462$