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Math Help - Find K in an equation like gcd(K,a)=gcd(K,b)+some constant

  1. #1
    SMR
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    Find K in an equation like gcd(K,a)=gcd(K,b)+some constant

    Suppose that K is an integer between 600000 and 800000 such that gcd(k,271)=gcd(k, 2010)+70.
    Find K.

    I know the answer should be K=708123 (I tested this in a C program with a for loop), but what are the steps I need to show for this question?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    gcd(a,b)=ax+by
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  3. #3
    SMR
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    Okay, so if I write down
    gcd(k, 271) = kx+ 271y, how can I proceed from there?
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