A quick one

  1. If a and b are relatively prime integers whose product is a square, show by means of an example that a and b are not necessarily squares. If they are not squares, what are they?

    Unless I read this question wrong I have not found and answer from 1 to 40... a little frustrated if anybody can help out.
     
  2. jcsd
  3. AKG

    AKG 2,585
    Science Advisor
    Homework Helper

    [tex]\mathbb{Z} = \{ 0,\, 1,\, \dots ,\, 40,\, 41\, \dots \}\ \mathbf{\cup \ \{-1,\, -2,\, \dots \}}[/tex]

    Start with the assumption that a and b are coprime integers whose product is square. What can you deduce about the prime factors of a and b? You should be able to deduce something almost like that a and b should both be square, but the fact that you're looking for integers will provide a loophole.
     
  4. To clarify you must account for the fact that integers are both negative and positive. Remember that a square can not be negative, but that coprime factors can.
     
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