Solve a Integer equation system

In summary, an integer equation system is a set of equations where the unknown values are integers. To solve it, you need to use algebraic techniques such as substitution, elimination, or graphing and simplify your solutions to ensure they are integers. The difference between an integer equation system and a linear equation system is that the former has only integer solutions while the latter can have fractions or decimals. Yes, an integer equation system can have multiple solutions, including infinite solutions. When solving an integer equation system, it is important to consider special cases such as no solutions, infinitely many solutions, and negative solutions.
  • #1
elimqiu
11
0
Find smallest [tex]d=2a^2=3b^3+2=5c^5+3 [/tex]
where a,b,c are integers.
This problem is very hard. Either no solution or d is toooooooo big
 
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  • #2
well, Chuck...?
 
  • #3

What is an integer equation system?

An integer equation system is a set of equations where the unknown values are integers. This means that the solutions to the equations must be whole numbers, not fractions or decimals.

How do you solve an integer equation system?

To solve an integer equation system, you need to use a combination of algebraic techniques such as substitution, elimination, or graphing. You must also make sure to follow the order of operations and simplify your solutions to make sure they are integers.

What is the difference between an integer equation system and a linear equation system?

An integer equation system is a type of linear equation system where the solutions must be integers. A linear equation system can have solutions that are fractions or decimals, while an integer equation system only has integer solutions.

Can an integer equation system have more than one solution?

Yes, an integer equation system can have multiple solutions. In fact, some integer equation systems may have an infinite number of solutions. It is important to check your answers and make sure they satisfy all of the equations in the system.

Are there any special cases to consider when solving an integer equation system?

Yes, there are a few special cases to consider when solving an integer equation system. These include systems with no solutions, systems with infinitely many solutions, and systems with negative solutions. It is important to be aware of these special cases and handle them accordingly when solving an integer equation system.

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