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Math Help - Group Theory - Prove that for ab-cd=1, there is no cancellation for (a+c)/(b+d)

  1. #1
    Junior Member
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    Group Theory - Prove that for ab-cd=1, there is no cancellation for (a+c)/(b+d)

    Hi, I have the following problem.

    "Prove that for any positive integers a, b, c, d satisfying

    ab-cd=1,

    no cancellation is possible in the fraction

    (a+c)/(b+d) (where the result of the fraction is a rational number."

    Well, I know how to cancel a fraction, but how am I supposed to do this one, and what letters should I use to prove the cancellation?

    I'd really appreciate it if you could give me a hand, thanks.
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  2. #2
    Senior Member roninpro's Avatar
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    A fraction cannot be canceled if the numerator and denominator have GCD 1. Can you show that \gcd(a+c,b+d)=1?
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