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Integers reachable by ax + by + 30xy

  1. Aug 21, 2008 #1
    I am working on a problem and encountered the following problem:
    Given a,b element of {1,7,11,13,17,19,23,29} and also given that :
    x,y element of N+{0}.
    Now I want to *formlulate* the numbers that are _not_ reachable by the equation :
    z = ax + by + 30xy

    The formula(tion) should tell instantly whether z is reachable or not for any z element N

    Any hints or even resolves are highly appreciated.
  2. jcsd
  3. Aug 21, 2008 #2


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    (a, b, x, y) = (1, 29, z, 0) shows that all z in N are reachable.
  4. Aug 21, 2008 #3
    All clear ... a discount on my side. Meant are a,b element of {7,11,13,17,19,23,29,31}, that is wo. the trivial option.
    Thank for your reply.
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