Integers reachable by ax + by + 30xy

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The discussion centers on determining integers that cannot be expressed in the form z = ax + by + 30xy, where a and b are selected from the set {1, 7, 11, 13, 17, 19, 23, 29} and x, y are non-negative integers. The user seeks a formulation that identifies unreachable integers z in the natural numbers (N). It is noted that for specific values of a and b, such as (1, 29), all integers z are reachable, indicating that the choice of a and b significantly impacts the reachability of z.

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mahch
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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.
 
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(a, b, x, y) = (1, 29, z, 0) shows that all z in N are reachable.
 
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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