2005 Canadian MO Problems/Problem 2: Difference between revisions

Revision as of 19:32, 28 July 2006

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 $(c/a + c/b)^2 = n$ .

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