Integers reachable by ax + by + 30xy

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In summary, the conversation discusses a problem involving the formulation of numbers that are not reachable by a given equation. The equation involves variables from specific sets and the goal is to determine if a given number is reachable or not. The conversation also mentions a specific example that shows all numbers in N are reachable, and clarifies the variables involved.
  • #1
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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  • #2
(a, b, x, y) = (1, 29, z, 0) shows that all z in N are reachable.
 
  • #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.
 

Related to Integers reachable by ax + by + 30xy

1. What is the definition of "Integers reachable by ax + by + 30xy"?

The phrase "Integers reachable by ax + by + 30xy" refers to a set of integers that can be obtained by plugging in different values for variables a, b, and x, and then adding them together with the product of 30 and the product of x and y.

2. How do you determine which integers are reachable by ax + by + 30xy?

To determine which integers are reachable by ax + by + 30xy, you can start by plugging in different values for a, b, and x, and then solving for the resulting integer. You can also use mathematical techniques such as factoring and substitution to find patterns and determine which integers are attainable.

3. Can negative integers be reachable by ax + by + 30xy?

Yes, negative integers can be reachable by ax + by + 30xy. This is because the variables a, b, x, and y can be negative, and when multiplied together, their products can result in a negative integer.

4. Are there any limitations to the values of a, b, and x for integers to be reachable by ax + by + 30xy?

There are no specific limitations to the values of a, b, and x for integers to be reachable by ax + by + 30xy. However, certain values may make it more difficult to reach certain integers or may result in a larger range of reachable integers.

5. How is the concept of "Integers reachable by ax + by + 30xy" useful in science?

The concept of "Integers reachable by ax + by + 30xy" can be useful in science in various ways. It can help in solving mathematical problems and equations, modeling and predicting patterns and phenomena in nature, and understanding the relationships between different variables and their effects on an outcome. It can also be applied in fields such as physics, chemistry, and biology for calculations and data analysis.

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