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    How do i prove a=bc+d with a,b,c,d belong to Z then gcd (a,b)=gcd(b,d)

    And how i prove or disprove the quantifier
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    isn't the first bit something to do with the euclidean algorithm? google it.
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    (Original post by kanz)
    How do i prove a=bc+d with a,b,c,d belong to Z then gcd (a,b)=gcd(b,d)
    Show that any common divisor of a and b is a divisor of d (as well as b) and any common divisor of b and d is a divisor of a (as well as b) so the two pairs have the same common divisors and hence the same greatest comon divisors.

    And how i prove or disprove the quantifier
    Your expression seems to say that any two subsets of the rationals are in bijection and thus have the same cardinality (so for finite sets the same number of elements). The answer should be clear.
 
 
 
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