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Math Help - Math proof regarding gcd

  1. #1
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    Exclamation Math proof regarding gcd

    Here is a problem :
    Prove if gcd (a,b) = e then gcd (a, b/e)= 1

    Hint : use the fact that gcd(a,bc)= gcd(a,b) gcd(a,c)

    Please help me I am lost
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Math proof regarding gcd

    Quote Originally Posted by tareksha View Post
    Here is a problem :
    Prove if gcd (a,b) = e then gcd (a, b/e)= 1

    Hint : use the fact that gcd(a,bc)= gcd(a,b) gcd(a,c)

    Please help me I am lost
    I have a counterexample: gcd (6, 4) = 2 but gcd (6, 4/2) = gcd (6, 2) = 2

    A counterexample for the hint would be: gcd (6, 4) = 2 whereas gcd (6, 2)*gcd (6, 2) = 4
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  3. #3
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    Re: Math proof regarding gcd

    Quote Originally Posted by alexmahone View Post
    I have a counterexample: gcd (6, 4) = 2 but gcd (6, 4/2) = gcd (6, 2) = 2

    A counterexample for the hint would be: gcd (6, 4) = 2 whereas gcd (6, 2)*gcd (6, 2) = 4

    Thank you so much brother . I appreciate your response
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