Which of the following is a Pythagorean triple?

Which of the following is a Pythagorean triple?
  1. $(3, 4, 5)$
  2. $(2, 3, 4)$
  3. $(4, 5, 6)$
  4. $(6, 7, 8)$

Solution

$3^{2} + 4^{2} = 9 + 16 = 25 = 5^{2}$. The others fail this test.

Asked in: IMO

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