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2bornot2b

  • 2 years ago

If gcd(a,b)=1 then prove that gcd(ac,b)=gcd(c,b)

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  1. FoolForMath
    • 2 years ago
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    HINT: (a,b) = 1 means that there is some x and y such that ax + by = 1

  2. satellite73
    • 2 years ago
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    perhaps start by writing \(d=gcd(ac,b)\) and \(e=gcd(b,c)\) and then show that \(d|e\) and \(e|d\)

  3. FoolForMath
    • 2 years ago
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    How about this: http://math.stackexchange.com/questions/20889/

  4. satellite73
    • 2 years ago
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    yes i guess that will do it. notice this fairly obvious fact actually takes a few lines to prove!

  5. FoolForMath
    • 2 years ago
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    Yes, sat, it's one of the many things of number theory which are just intuitively plausible.

  6. 2bornot2b
    • 2 years ago
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    what do you mean @FoolForMath

  7. FoolForMath
    • 2 years ago
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    If you see Sivaram's answer, he has used the same fact I alluded to you :)

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