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Thread: 1/2005

  1. #1
    Aug 2005

    Need Help!!!

    1/a + 1/ab = 1/2005
    Which nos can be a or b?
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  2. #2
    Junior Member
    Aug 2005



    I see this kind of problem has already appeared not long ago in the forums.
    Well, the key is always to remove the fractions and factorize.
    1) remove the fractions:
    1/a+1/ab=1/2005 to remove all denominators we multiply both sides by 2005ab so we get 2005b+2005=ab
    2) factorize:
    we put first the bs together 2005=ab-2005b and then we factorize b :

    Now there has to be a shortcut. We can not ask you to find barehanded tens of integers. So we see that b multiplied by (a-2005) gives 2005 so b is a factor of 2005 and (a-2005) also is a factor of 2005.
    So we search for the prime factorization of 2005 which is 2005=5*401 (I think that 401 is prime)
    So we do not have many choices : either b=5 and so (a-2005)=401 or b=401 and (a-2005)=5 so we find "a" and we get two choices :

    b=5 and a=2406
    b=401 and a=2010

    Always remove the fractions, factorize and then work with the factors .

    Good luck

    Sorry I missed two :
    b=1 and (a-2005) = 2005 so b=1 and a=4010
    b=2005 and (a-2005) = 1 so b=2005 and a=2006
    Last edited by hemza; Sep 10th 2005 at 06:40 AM.
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