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Shahrooz
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By Matiyasevich's theorem, each member of computably enumerable set can be obtain from a diophantine equation system. For prime numbers, this system of diophantine equation is found. My question is: For

For special computably enumerable set as like as square numbers or perfect numbers, how can we construct this diophantine equation system?

Is there Matiyasevich's type theorem for the matrix algebra?

By Matiyasevich's theorem, each member of computably enumerable set can be obtain from a diophantine equation system. For prime numbers, this system of diophantine equation is found. My question is: For special computably enumerable set as like as square numbers or perfect numbers, how can we construct this diophantine equation system?

By Matiyasevich's theorem, each member of computably enumerable set can be obtain from a diophantine equation system. For prime numbers, this system of diophantine equation is found. My question is:

For special computably enumerable set as like as perfect numbers, how can we construct this diophantine equation system?

Is there Matiyasevich's type theorem for the matrix algebra?

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Shahrooz
  • 4.8k
  • 1
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  • 36

Diophantine equation for generating computably enumerable set

By Matiyasevich's theorem, each member of computably enumerable set can be obtain from a diophantine equation system. For prime numbers, this system of diophantine equation is found. My question is: For special computably enumerable set as like as square numbers or perfect numbers, how can we construct this diophantine equation system?