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A quick oneby bobsmiters
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#1
Oct2405, 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. 


#2
Oct2405, 02:48 AM

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P: 2,586

[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. 


#3
Oct2405, 11:29 PM

P: 894




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