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2005 Canadian MO Problems/Problem 2

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Problem

Let $(a,b,c)$ be a Pythagorean triple, i.e., a triplet of positive integers with $a^2+b^2=c^2$.

  • Prove that $(c/a + c/b)^2 > 8$.
  • Prove that there does not exist any integer $n$ for which we can find a Pythagorean triple $(a,b,c)$ satisfying $(c/a + c/b)^2 = n$.

Solution

See also

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