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A quick one

by bobsmiters
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bobsmiters
#1
Oct24-05, 02:07 AM
P: 12
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.
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AKG
#2
Oct24-05, 02:48 AM
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[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.
ramsey2879
#3
Oct24-05, 11:29 PM
P: 894
Quote Quote by AKG
[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.
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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